what is the boiling point of a solution that contains each of the following quantity of solute in 1.00 kg of water?

Answers

Answer 1

The boiling point of a solution that contains each of the following quantity of solute in 1.00 kg of water is depending on factors such as pressure and the specific solute used..

The boiling point of a solution depends on the amount of solute dissolved in it. Here are the boiling points for various quantities of solute in 1.00 kg of water:

a. For a solution with 1 mole of a non-electrolyte solute (such as glucose), the boiling point elevation is approximately 0.51 °C. Therefore, the boiling point of this solution would be 100.51 °C.

b. For a solution with 1 mole of an electrolyte solute (such as NaCl), the boiling point elevation is approximately 0.52 °C. Therefore, the boiling point of this solution would be 100.52 °C.

c. For a solution with 1 gram of a non-electrolyte solute (such as glucose), the boiling point elevation is approximately 0.002 °C. Therefore, the boiling point of this solution would be 100.002 °C.

d. For a solution with 1 gram of an electrolyte solute (such as NaCl), the boiling point elevation is approximately 0.0021 °C. Therefore, the boiling point of this solution would be 100.0021 °C.

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Related Questions

What are hydrocarbons made of

A: Water and carbon

B: Hydrogen, oxygen, and carbon

C: Hydrogen and carbon

D: Carbon and halogens

Answers

Answer: Hydrogen and carbon

Explanation:

7200 years ago, the ratio of 14c to 12c in the atmosphere was 10% higher than it is today. a piece of wood is known to be 7200 years old. part a part complete if its age were determined using radiocarbon dating, how old would it appear to be? (the variation in atmospheric 14c with time is well understood and is corrected for in actual radiocarbon dating.)

Answers

The ratio of 14C to 12C in the atmosphere is constant, but it can vary over time due to factors such as solar activity and changes in the Earth's magnetic field.

It is known that 7200 years ago, the ratio of 14C to 12C in the atmosphere was 10% higher than it is today. This means that the piece of wood, which is also 7200 years old, would contain more 14C than a piece of wood from today. However, when using radiocarbon dating, the variation in atmospheric 14C with time is well understood and is corrected for in actual radiocarbon dating. Therefore, the age of the wood would appear to be 7200 years old, even though the ratio of 14C to 12C was higher 7200 years ago.


Step 1: Understand that 7200 years ago, the ratio of 14C to 12C in the atmosphere was 10% higher than today.
Step 2: Radiocarbon dating works by measuring the ratio of 14C to 12C in a sample and comparing it to the current atmospheric ratio.
Step 3: Due to the higher ratio of 14C to 12C in the atmosphere 7200 years ago.

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n radiocarbon dating, the ratio of 14C to 12C in an organism is compared to the ratio in the atmosphere at the time the organism was alive.

Since the ratio of 14C to 12C in the atmosphere has changed over time, it is necessary to correct for this variation when determining the age of a sample.Given that 7200 years ago, the ratio of 14C to 12C in the atmosphere was 10% higher than it is today, we can use this information to correct for the change in atmospheric 14C levels.Let's denote the current ratio of 14C to 12C in the atmosphere as R_now, and the ratio 7200 years ago as R_then.

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how much heat is produced if 7.0 moles of ethane undergo complete combustion?

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The balanced equation for the combustion of ethane, C2H6, is: C2H6 + 3O2 → 2CO2 + 3H2OTo determine how much heat is produced if 7.0 moles of ethane undergo complete combustion, we need to use the balanced equation and the standard enthalpies of formation of the reactants and products.

The standard enthalpy of formation of a compound is the enthalpy change when one mole of the compound is formed from its constituent elements, with all reactants and products in their standard states (usually at 1 atm and 25°C).The standard enthalpies of formation of the reactants and products in the combustion of ethane are:

ΔHf°(C2H6) = -84.68 kJ/mol

ΔHf°(O2) = 0 kJ/mol

ΔHf°(CO2) = -393.51 kJ/mol

ΔHf°(H2O) = -285.83 kJ/mol

Now we can calculate the heat produced by using the difference between the enthalpies of the products and reactants:

2CO2 + 3H2O - (C2H6 + 3O2)

ΔH = 2(-393.51 kJ/mol) + 3(-285.83 kJ/mol) - (-84.68 kJ/mol + 3(0 kJ/mol))

ΔH = -1560.78 kJ/mol

Therefore, if 7.0 moles of ethane undergo complete combustion, the amount of heat produced will be:

-1560.78 kJ/mol x 7.0 mol

= -10,925.46 kJ or -10,925,460 J.

Note that the negative sign indicates that heat is released by the reaction, which is exothermic.

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Charles's law describes the relationship of the volume and temperature of
gas at a constant mass and pressure. According to this law, what would
happen to the temperature of the gas if its volume decreased from 1.0 L to
0.50 L?
O A. The temperature would decrease by 500 K.
O B. The temperature would double.
O C. The temperature would be reduced by half.
O D. The temperature would increase from 500 K to 1000 K.

Answers

Answer:

The temperature would be reduced by half

Explanation:

Charles' Law => V ∝ T =>  V = kT => k = V/T

For two sets of T vs V conditions, the system constant (k) remains unchanged and k₁ = k₂ => V₁/T₁ = V₂/T₂.

Therefore, if V₁ is reduced to 1/2V₁ = V₂ => V₁/T₁ = 1/2V₁/T₂ => V₁/T₁ = V₁/2T₂

and solving for T₂ =>  1/T₁ = 1/2T₂ => 2T₂ = T₁ => T₂ = 1/2T₁

∴ The initial temperature (T₁) would be reduced by half or, T₂ = 1/2T₁

What is Keq for the reaction N₂ + 3H2 = 2NH3 if the equilibrium
concentrations are [NH3] = 3 M, [N₂] = 2 M, and [H₂] = 1 M?

Answers

The equilibrium constant, Keq, for the reaction is 13.5.

What is Keq for a reaction?

The equilibrium constant, Keq, for a reaction is the value of a chemical reaction's reaction quotient at chemical equilibrium, which is a condition that a dynamic chemical system approaches when enough time has passed and at which its composition has no discernible tendency to change further.

For a reaction: A + B ⇆ C + D

Keq = [C] [D] / [A] [B]

For the given reaction,  N₂ + 3 H₂ ⇆ 2 NH₃

where the equilibrium concentrations are;

[N₂] = 2 M

[H₂] = 1

[NH₃] = 3

Keq; 3³ / (2 * 1³)

Keq = 13.5

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Help with this please it’s due at 11:59pm tonight

Help with this please its due at 11:59pm tonight

Answers

The molecular structure of the covalent molecules, as well as the electron dot diagrams of hydrogen, ammonia, hydrochloric acid, water, and methane, are found in the attachment.

What are covalent molecules?

Covalent molecules are molecules that are formed by covalent bonds between two or more atoms of the same or different elements.

The inorganic elements hydrogen, fluorine, chlorine, water, and ammonia as well as all organic compounds are examples of molecules with covalent connections.

A covalent bond is formed when two atoms exchange one or more pairs of electrons. The two atomic nuclei are concurrently drawing these electrons to them. When the difference between the electronegativities of two atoms is too tiny for an electron transfer to take place to create ions, a covalent bond is formed.

In electron dot diagrams, the valence electrons of an atom are represented by dots that are positioned all around the symbol of the element.

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Help with this please its due at 11:59pm tonight
Help with this please its due at 11:59pm tonight
Help with this please its due at 11:59pm tonight
Help with this please its due at 11:59pm tonight
Help with this please its due at 11:59pm tonight

A coca-cola contains 150 000 calories. convert this to calories.

Answers

im pretty sure the right answer would be 150, but correct me if im wrong please!

Use the calculated masses of the anhydrous compound and water (from #1) and the identity of the hydrated compound (on the provided data slip) to determine the formula of the hydrated compound
Mass of anhydrous compound (from #1): ____
Mass of water lost (from #1): ______
A. Calculate moles of the anhydrous compound (MgSO4):
B. Calculate moles of water:
C. Determine the simplest mole ratio to find the empirical formula:
(Note: unlike with determining formulas for compounds, you may round to the nearest whole number for the moles of water in the hydrate)

Answers

The empirical formula of the hydrated compound would be MgSO4·2H2O.

To determine the formula of the hydrated compound, we first need to know the mass of the anhydrous compound and water lost. Once we have these values, we can calculate the moles of each compound using their molar masses.
Assuming the mass of the anhydrous compound is provided in the question, we can calculate the mass of water lost by subtracting the mass of the anhydrous compound from the total mass of the hydrated compound.
Next, we can calculate the moles of the anhydrous compound (MgSO4) using its molar mass (120.37 g/mol) and the given mass of the anhydrous compound. The formula to calculate the moles is:
Moles of anhydrous compound = mass of anhydrous compound / molar mass of anhydrous compound
Similarly, we can calculate the moles of water using its molar mass (18.02 g/mol) and the given mass of water lost. The formula to calculate the moles is:
Moles of water = mass of water lost / molar mass of water
Now, to determine the simplest mole ratio between the anhydrous compound and water, we divide the moles of each compound by the smallest value. This gives us the empirical formula of the hydrated compound. For example, if we calculate that there are 3 moles of MgSO4 and 6 moles of water, we would divide both values by 3 to get a mole ratio of 1:2. Therefore, the empirical formula of the hydrated compound would be MgSO4·2H2O.
In summary, to determine the formula of a hydrated compound, we need to know the mass of the anhydrous compound and water lost, calculate the moles of each compound, and then determine the simplest mole ratio to find the empirical formula.

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The molecular formula of the hydrated compound would be (MgSO4)1(H2O)7 or MgSO4.7H2O.

To determine the formula of the hydrated compound, we need to use the masses of the anhydrous compound and water from #1 and the identity of the hydrated compound on the provided data slip. Let's assume that the mass of the anhydrous compound is X and the mass of water lost is Y.

A. To calculate moles of the anhydrous compound (MgSO4), we need to divide the mass by its molar mass. The molar mass of MgSO4 is 120.37 g/mol. Therefore, moles of anhydrous compound = X/120.37.

B. To calculate moles of water, we need to divide the mass of water lost by its molar mass. The molar mass of water is 18.02 g/mol. Therefore, moles of water = Y/18.02.

C. The empirical formula of the hydrated compound can be determined by finding the simplest mole ratio between the anhydrous compound and water. Divide the moles of each compound by the smallest value and round to the nearest whole number. Let's assume that the mole ratio of anhydrous compound to water is a:b. Then, a:X/120.37 = b:Y/18.02. Simplifying this equation gives a:b = Y/18.02X/(120.37- Y).

Using the identity of the hydrated compound on the provided data slip, we can determine the molecular formula of the hydrated compound. For example, if the hydrated compound is MgSO4.7H2O, then the empirical formula would be MgSO4:H2O = 1:7. Therefore, the molecular formula of the hydrated compound would be (MgSO4)1(H2O)7 or MgSO4.7H2O.

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Which statements accurately describe volume? Check all that apply. Volume is a physical property of an object. Volume is measured using a balance. The volume of a solid changes with the shape of the container. One unit of volume is the milliliter. Liquids and solids have constant volumes.

Answers

Answer:

- Volume is a physical property of an object.

- One unit of volume is the milliliter.

- Liquids and solids have constant volumes.

Explanation:

Statement that are true about volume are;

Volume is a physical property of an object.One unit of volume is the milliliter.Solids have constant volumes.

What is volume?

volume can be regarded as a 3-dimensional space enclosed by a boundary or occupied by an object.

Therefore, Volume is a physical property of an objec and One unit of volume is the milliliter.

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What would be the nitrogen balance of an active, healthy adult body where body weight and lean body mass are not changing?
A. Nitrogen unbalanced
B. Nitrogen equilibrium
C. Negative nitrogen balance
D. Positive nitrogen balance

Answers

The nitrogen balance of an active, healthy adult body where body weight and lean body mass are not changing would be B. Nitrogen equilibrium.

Nitrogen balance refers to the difference between nitrogen intake and nitrogen excretion in the body. When an individual is in nitrogen equilibrium, it means that the nitrogen intake from dietary protein and other sources is equal to the nitrogen excretion through various routes, such as urine, feces, and sweat.

In an active, healthy adult body where body weight and lean body mass are stable, the nitrogen intake would be sufficient to meet the body's nitrogen needs, which include protein synthesis for tissue repair and maintenance. The nitrogen excretion would also be balanced, with the amount of nitrogen excreted being equal to the amount of nitrogen taken in.

Therefore, when the nitrogen intake and excretion are in equilibrium, it indicates a state of nitrogen balance in the body. This means that the body is neither gaining nor losing nitrogen, and the individual is maintaining their current body weight and lean body mass.

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In an active, healthy adult body where body weight and lean body mass are not changing, the nitrogen balance would be in a state of (B) nitrogen equilibrium.

Nitrogen balance refers to the balance between nitrogen intake and nitrogen excretion in the body. Nitrogen is primarily obtained through dietary protein intake and is excreted through urine, feces, and sweat.

In a state of nitrogen equilibrium, the amount of nitrogen intake from dietary protein matches the amount of nitrogen excretion, resulting in a stable balance. This indicates that the body is neither gaining nor losing nitrogen over time.

A balanced nitrogen state is generally considered favorable for overall health and maintenance of lean body mass. It suggests that the body's protein needs are being adequately met to support various physiological processes, including tissue repair, muscle synthesis, and immune function.

Therefore, in the given scenario, the nitrogen balance would be categorized as nitrogen equilibrium.

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if a drop of carbonated water were placed on blue litmus paper, what would be the color of the litmus paper?

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If a drop of carbonated water were placed on blue litmus paper, the color of the litmus paper will turn red.

Carbonated water is water that contains dissolved carbon dioxide gas, which may have been added to the water intentionally under pressure or may have occurred naturally as a result of geological processes. Carbonation creates tiny bubbles that make water effervescent. Club soda, sparkling natural water, and sparkling water created commercially are examples of soda water.

As soda water is an acidic solution, the blue litmus paper changes to a red color. This is because the carbonation process, in which CO₂ is bubbled into the water, results in the formation of carbonic acid, which then interacts with litmus paper.

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How many electrons are in 30 grams of water.

Answers

There should be 1025 grams

compare protons neutrons and electrons to a family or a business​

Answers

Protons have the same amount of electrons as electrons

how do you determine valence electrons of a metal? A non Metal?

Answers

Answer:

Check the electronic configuration of elements.

Explanation:

Valence electrons are the elwctrons present in the outermost shell of any element.

For example,

Electronic Configuration of Sodium = 2,8,1

Here , Sodium has 1 valence electrons.

Valency of an element is the total no. of electrons to be gained/losed in order to achieve duplet/octate state.

For example,

Electronic configuration of Sodium = 2,8,1

Sodium can achieve octate state either by losing 1 electron or gaining 7 electrons. But losing 1 electron is eay than gaining 7 electrons. So Valency of Sodium = +1

Metals have 1 or 2 or 3 valence electrons.

Non metals have 4 or 5 or 6 or 7 valence electrons.

Noble gases tend to stay in duplet/octate state i.e they have 2 or 8 valence electrons.

How many hydrogen atoms are in 2h2+02—2h20?

Answers

Answer: Two hydrogen atoms

Explanation:

A water molecule (formally known as dihydrogen monoxide) is composed of two hydrogen atoms and one oxygen atom. But you can't simply take two hydrogen atoms and stick them onto an oxygen atom. The actual reaction to make water is a bit more complicated: 2H2 + O2 = 2H2O + Energy.

How are superheavy elements made?​

Answers

Answer: Most methods for making new elements involve a cyclotron, which speeds up atoms to high velocities before they smash into other atoms—these atoms are usually of different elements. This causes the nuclei to combine, creating new heavier elements.

Explanation: How are superheavy elements made?​

Methyl isocyanate is used in the industrial synthesis of a type of pesticide and herbicide known as a carbamate. As a historical note, an industrial accident in Bhopal, India in 1984 resulted in leakage of an unknown quantity of this chemical into the air. An estimated 200,000 persons were exposed to its vapors and over 2000 of these people died.
Methyl isocyanate reacts with strong acids, such as sulfuric acid, to form a cation. For protonation on O , which resonance contributor is most important?

Answers

Protonation of isocyanate happens on Oxygen atom. Here the nitrogen atom attached to the carbocation is the resonance contributor

Methyl isocyanate is a  precursor or intermediate in the production of carbamate, which is a popular pesticide and herbicide. Protonation happens in the carbenium ion, or carbocation, since it is sp hybridized with oxygen and nitrogen.( Image is given below)

There are two contributing resonance structures in the image. The protonation of nitrogen leads to a formation of resonance structure with triple bond on oxygen, which is very unlikely. The other structure contributes to the formation of protonated product, since triple bonded nitrogen atom is very likely to form.

So nitrogen is the resonance contributor for the protonation of oxygen.

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Methyl isocyanate is used in the industrial synthesis of a type of pesticide and herbicide known as a

D Question 3 What is the correct IUPAC name of the following compound? CI- Problem viewing the image, Click Here O 7-chlorohept-(3E)-en-1-yne O 7-chlorohept-(3Z)-en-1-yne O 1-chlorohept-(4E)-en-6-yne

Answers

The correct IUPAC name of the compound is 7-chlorohept-(3E)-en-1-yne.

The IUPAC name of a compound is determined by following a set of rules established by the International Union of Pure and Applied Chemistry (IUPAC). To determine the correct name of the compound given, we need to analyze its structure and identify the functional groups, substituents, and their positions.

In this case, the compound has a chain of seven carbon atoms (hept) with a chlorine atom (chloro) attached at the 7th position. It also contains a triple bond (yne) and a double bond (en) on adjacent carbon atoms. The stereochemistry of the double bond is indicated by the E configuration, which means that the two highest priority substituents are on opposite sides of the double bond.

Therefore, the correct IUPAC name of the compound is 7-chlorohept-(3E)-en-1-yne.

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What happens to the particles of a solid when the solid changes into a liquid? (5 points) a They increase in size. b They decrease in size. c The attractive force between them increases. d The attractive force between them decreases.

Answers

The answer is D, the attractive force between them decreases.

Although the volume that the particles take up generally increases when going from solid to liquid, particles themselves never change their size. It’s the attractive force that decreases and doesn’t pull the particles together as tightly when a solid changes to liquid.

Why is the atomic theory important?

Answers

Answer: As we know that atoms are the building block of the universe and so it is very important to know about the structure of atom so that we can understand and explain the matter, properties of matter and reaction/change between matter and atomic theory is one of the step to understand matter that taken by chemist and physicist

HELP ME PLEASE ASAP I NEED HELP WITH QUESTION 1.2

HELP ME PLEASE ASAP I NEED HELP WITH QUESTION 1.2

Answers

The section of the periodic table in Figure 1 that is most likely to contain element R is section A.

What is the explanation about above answer?Based on the information you provided, element Q is a dull solid with a melting point of 44 °C and does not conduct electricity. These properties suggest that element Q is likely a non-metal. Therefore, the section of the periodic table in Figure 1 that is most likely to contain element Q is section B. This is because non-metals have a low melting and boiling point and they are poor conductors of electricity.Regarding element R, the information provided is its formula R2+ and R3+. These formulas suggest that element R is likely a metal and has a positive charge. Therefore, the section of the periodic table in Figure 1 that is most likely to contain element R is section A. This is because most of the elements in section A are metals and they have positive charges. Since the given information is not enough to determine the position of the element R precisely, however, it's likely that section A is the most probable one.

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Please answer the following question using the data below: H2O vapor content: 13 grams H2O vapor capacity: 52 grams at 25 degrees Celsius 13 grams at 10 ∘
C 52 grams at 30 ∘
C What is the dew point for the conditions listed above? LCL 3π5 25C Relative Humidity =100%

Answers

Given data:H2O vapor content: 13 gramsH2O vapor capacity: 52 grams at 25 degrees Celsius 13 grams at 10∘C52 grams at 30∘CFormula used to find the dew point:$$\dfrac{13}{52}=\dfrac{(A*3\pi)/(ln100)}{(17.27-A)}$$$$\frac{1}{4}=\dfrac{(A*3\pi)/(ln100)}{(17.27-A)}$$

Where A is the constantDew Point:It is the temperature at which air becomes saturated with water vapor when the temperature drops to a point where dew, frost or ice forms. To solve this question, substitute the given data into the formula.$$13/52=\dfrac{(A*3\pi)/(ln100)}{(17.27-A)}$$$$13(17.27-A)=3\pi A(ln100)$$By simplifying the above expression, we get$$A^2-17.27A+64.78=0$$Using the quadratic formula, we get$$A=9.9,7.4$$

The dew point is 7.4 since it is less than 10°C.More than 100:The term "More than 100" has not been used in the question provided.

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If you were asked to dry fish to make a smoked one, where are you going to put it? Is it nearing a dry cool place or wet warm place? Why?​

Answers

If I were asked to dry fish to make a smoked one, I would place it in a dry and cool place. This is because the process of smoking fish involves first drying it out to remove excess moisture, which helps to preserve the fish and prevents it from spoiling. A dry and cool environment is ideal for this, as it allows the moisture to evaporate slowly without the risk of the fish becoming too warm and potentially spoiling.

On the other hand, a wet and warm environment would be counterproductive, as it would encourage the growth of bacteria and other microorganisms that could spoil the fish before it has a chance to be properly preserved through the smoking process. Therefore, it is important to find a cool and dry location to dry the fish before smoking it, which can include a well-ventilated room or an outdoor area that is protected from direct sunlight and rain.

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1. When NaCl are diolved in water, the freezing point i found to be - 0. 26°C. What i the omolarity for thi olution?
The K for water i 1. 86

Answers

The freezing point of water after NaCl has been dissolved in it is determined to be - 0.26°C. This solution has a 0.02 mol molarity.

The molality is the proportion of solute, in your case sodium chloride, NaCl, to solvent, in this case water, expressed as the number of moles per kilogram.

Utilizing the substance's molar mass will allow you to determine how many moles of sodium chloride are present in the sample. 25g = 1 mole of NaCl; 58.44g = 0.42 moles of NaCl

You then understand that you are dissolving many moles of sodium chloride in 20 kg of water.

To determine how many moles of solute are present in 1 kilogram of water, utilize the composition of this solution.

0.428 moles of NaCl per kilogram of water. 20 kg water

= 0.0214 moles of sodium chloride

= 0.02 mol

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what is the scientific name for the layers of gas that surrounds the earth ?

a . biosphere

b . atmosphere

c . lithosphere

d . hydrosphere


PLEASEE ANSWER ILL GIVE U BRAINLYEST ASPAAAAPP

Answers

Answer:

Hey mate.....

Explanation:

This is ur answer.....

b. Atmosphere

An atmosphere is the layers of gases surrounding a planet or other celestial body. Earth's atmosphere is composed of about 78% nitrogen, 21% oxygen, and one percent other gases.

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What is the elevation of point x on rock mountain ( Ik it's blury but please help for 30 points ) ty

What is the elevation of point x on rock mountain ( Ik it's blury but please help for 30 points ) ty

Answers

Explanation:

A contour map shows two locations, X and Y, 5 kilometers apart. The elevation at location X is 800 meters and the elevation at location Y is 600 meters.

How many mls of solvent are required to make a 48% solution from 25 g of solute? (round to the nearest tenth with no units!)

Answers

To make a 48% solution from 25 g of solute, you would need approximately 52.08 mL of solvent.

To calculate the volume of solvent required, we need to consider the mass percent of the solution. The mass percent is defined as the ratio of the mass of solute to the total mass of the solution, multiplied by 100. In this case, the mass percent is given as 48%.

To find the volume of solvent, we can set up a proportion using the mass percent. Let's assume the total volume of the solution is V mL. We can set up the following equation:

(25 g)/(V mL) = (48 g)/(100 mL)

Cross-multiplying and solving for V, we get:

25V = 48 * 100

V = (48 * 100)/25

V ≈ 192 mL

Therefore, you would need approximately 192 mL of the solvent to make a 48% solution from 25 g of solute.

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A heated metal object his temperature is 120 C is dropped into a tub of water who’s temperature is 10c which of the following will most likely occur

Answers

Answer:

exchange of heat

Explanation:

as metal is at high temprature therefore it will lose heat and will be absorbed by the water

Explain how density can be used to differentiate between pure substances and mixtures?​

Answers

A pure substance would be denser than a substance with added mixtures.

A chemist, Dr. V.A. Pore, wishes to detect an impurity in a certain compound that she is making. There is a test that has sensitivity of 0.9 and specificity of 0.95. That is, the test is positive for an impurity when an impurity is present 90% of the time, and the test is negative for an impurity when no impurity is present 95% of the time. About 15\% of Dr. Pore's compounds contain an impurity. 9. A compound is selected at random from Dr. Pore's output. The test indicates that an impurity is present. What is the conditional probability that the selected compound actually has an impurity? 1 10. Another compound is selected at random from Dr. Pore's output. The test indicates that an impurity is not present. What is the conditional probability that the selected compound is actually free of an impurity? 11. Two processes of a company produce rolls of materials. The rolls of Process I are 3% defective, and the rolls of Process II are 1% defective. Process I produces 60% of the company's output, Process II 40%. A roll is selected at random from the total output. Given that this roll is defective, what is the conditional probability that it is from Process I?

Answers

The correct options are:1.

Conditional probability that the selected compound actually has an impurity is 0.74.2.

Conditional probability that the selected compound is actually free of an impurity is 0.0185.3.

Conditional probability that the selected roll is from Process I given that it is defective is 0.64.

Here, we need to find out the probability that a selected compound has an impurity given that the test indicates an impurity is present.

P(A) = probability that a compound has impurity = 0.15

P(B) = probability that the test indicates an impurity is present

= 0.15 x 0.9 + 0.85 x 0.05

= 0.14 + 0.0425

= 0.1825P

(B|A) = probability that the test indicates an impurity is present given that the compound has impurity = 0.9

Therefore, by Bayes' Theorem,

P(A|B) = P(B|A) * P(A) / P(B)

         = 0.9 * 0.15 / 0.1825

         = 0.7370

         ≈ 0.74

Conditional probability that the selected compound actually has an impurity is 0.74.10.

Here, we need to find out the probability that a selected compound is actually free of an impurity given that the test indicates an impurity is not present.

P(A) = probability that a compound has impurity = 0.15

P(B) = probability that the test indicates an impurity is not present = 0.85 x 0.95 + 0.15 x 0.1 = 0.8075

P(B|A) = probability that the test indicates an impurity is not present given that the compound has impurity

          = 0.1

Therefore, by Bayes' Theorem,

P(A|B) = P(B|A) * P(A) / P(B)

          = 0.1 * 0.15 / 0.8075

          = 0.0185

Conditional probability that the selected compound is actually free of an impurity is 0.0185.11.

Here, we need to find out the probability that the selected roll is from Process I given that it is defective.

Let A denote the event that a roll is from Process I and B denote the event that a roll is defective.

Then, we need to find out P(A|B).

P(A) = probability that a roll is from Process I = 0.6

P(B|A) = probability that a roll is defective given that it is from Process I = 0.03

P(B|A') = probability that a roll is defective given that it is from Process II = 0.01

P(A'|B) = probability that a roll is from Process II given that it is defective

Therefore, by Bayes' Theorem,

P(A|B) = P(B|A) * P(A) / [P(B|A) * P(A) + P(B|A') * P(A')]

= 0.03 * 0.6 / (0.03 * 0.6 + 0.01 * 0.4)

= 0.6429

≈ 0.64

Conditional probability that the selected roll is from Process I given that it is defective is 0.64.

Hence, the correct options are:1.

Conditional probability that the selected compound actually has an impurity is 0.74.2.

Conditional probability that the selected compound is actually free of an impurity is 0.0185.3.

Conditional probability that the selected roll is from Process I given that it is defective is 0.64.

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