A 2.500×10−2M solution of NaCl in water is at 20.0∘C. The sample was created by dissolving a sample of NaCl in water and then bringing the volume up to 1.000 L. It was determined that the volume of water needed to do this was 999.3mL . The density of water at 20.0∘C is 0.9982 g/mL.

A) Calculate the molality of the salt solution.
B) Calculate the mole fraction of salt in this solution.
C) Calculate the concentration of the salt solution in percent by mass.
D) Calculate the concentration of the salt solution in parts per million.

A) Why did the scarecrow win an award? Because he was outstanding in his field! Now, let's calculate the molality of the salt solution.

Molality is defined as the number of moles of solute (NaCl) per kilogram of solvent (water).

First, we need to calculate the moles of NaCl in the solution. The molarity of the solution is 2.500×10−2M, and the volume of the solution is 1.00 L. Therefore, the moles of NaCl can be calculated as:

moles of NaCl = molarity x volume
= 2.500×10−2 mol/L x 1.00 L
= 0.025 mol

Next, we need to calculate the mass of water in the solution. The density of water is given as 0.9982 g/mL, and the volume of water is 999.3 mL. Therefore, the mass of water can be calculated as:

mass of water = density x volume of water
= 0.9982 g/mL x 999.3 mL
= 998.5 g

Finally, we can calculate the molality of the salt solution:

molality = moles of NaCl / mass of water (in kg)
= 0.025 mol / (998.5 g / 1000)
= 0.025 mol / 0.9985 kg
= 0.0251 mol/kg

Thus, the molality of the salt solution is approximately 0.0251 mol/kg.

B) Why don't scientists trust atoms? Because they make up everything! Now, let's calculate the mole fraction of salt in this solution.

Mole fraction (X) is defined as the moles of a component (NaCl) divided by the sum of the moles of all components in the solution.

The moles of NaCl are already calculated to be 0.025 mol. The moles of water can be calculated as:

moles of water = mass of water (in grams) / molar mass of water
= 998.5 g / 18.015 g/mol (molar mass of water)
= 55.48 mol

The mole fraction of salt in the solution:

X(NaCl) = moles of NaCl / (moles of NaCl + moles of water)
= 0.025 mol / (0.025 mol + 55.48 mol)
= 0.000451

Thus, the mole fraction of salt in this solution is approximately 0.000451.

C) Why couldn't the bicycle find its way home? Because it lost its bearings! Now, let's calculate the concentration of the salt solution in percent by mass.

The percent by mass is determined by the mass of the solute (NaCl) divided by the mass of the solution, multiplied by 100.

Mass of NaCl = moles of NaCl x molar mass of NaCl
= 0.025 mol x 58.443 g/mol (molar mass of NaCl)
= 1.461 g

Mass of solution = mass of water + mass of NaCl
= 998.5 g + 1.461 g
= 999.96 g

Concentration of the salt solution in percent by mass:

% by mass = (mass of NaCl / mass of solution) x 100
= (1.461 g / 999.96 g) x 100
= 0.1461%

Thus, the concentration of the salt solution in percent by mass is approximately 0.1461%.

D) Did you hear about the mathematician who's afraid of negative numbers? He will stop at nothing to avoid them! Now, let's calculate the concentration of the salt solution in parts per million.

Parts per million (ppm) is determined by the mass of the solute (NaCl) divided by the mass of the solution, multiplied by 1,000,000.

Concentration of the salt solution in parts per million:

ppm = (mass of NaCl / mass of solution) x 1,000,000
= (1.461 g / 999.96 g) x 1,000,000
= 1,461 ppm

Thus, the concentration of the salt solution in parts per million is 1,461 ppm.

To solve this problem, we need to use various formulas and conversion factors. Let's go through each part step-by-step.

A) To calculate the molality of the salt solution, we'll use the formula:

Molality (m) = moles of solute / mass of solvent (in kg)

First, let's calculate the moles of NaCl in the solution:

moles of NaCl = concentration of NaCl (in M) * volume of solution (in L)

Given:
Concentration of NaCl = 2.500×10^(-2) M
Volume of solution = 1.000 L

moles of NaCl = (2.500×10^(-2) M) * (1.000 L)
moles of NaCl = 0.025 mol

Next, let's calculate the mass of water in kg:

mass of water = volume of water * density of water

Given:
Volume of water = 999.3 mL
Density of water = 0.9982 g/mL

mass of water = (999.3 mL) * (0.9982 g/mL)
mass of water = 998.5056 g

Now, let's convert the mass of water to kg:

mass of water = 998.5056 g * (1 kg / 1000 g)
mass of water = 0.9985056 kg

Finally, we can calculate the molality:

Molality (m) = moles of NaCl / mass of water (in kg)
Molality (m) = 0.025 mol / 0.9985056 kg
Molality (m) ≈ 0.0251 mol/kg

Therefore, the molality of the salt solution is approximately 0.0251 mol/kg.

B) To calculate the mole fraction of salt (NaCl) in the solution, we'll use the formula:

Mole fraction (X) = moles of solute / total moles of all components

The total moles of all components is the sum of the moles of NaCl and moles of water.

Given:
Moles of NaCl = 0.025 mol

First, let's calculate the moles of water:

moles of water = mass of water / molar mass of water

The molar mass of water (H₂O) is 18.015 g/mol.

moles of water = 998.5056 g / 18.015 g/mol
moles of water ≈ 55.455 mol

Now, we can calculate the mole fraction:

Mole fraction (X) = 0.025 mol / (0.025 mol + 55.455 mol)
Mole fraction (X) ≈ 4.52×10^(-4)

Therefore, the mole fraction of salt in this solution is approximately 4.52×10^(-4).

C) To calculate the concentration of the salt solution in percent by mass, we'll use the formula:

Percent by mass = (mass of solute / mass of solution) * 100

Given:
Mass of water = 998.5056 g

First, let's calculate the mass of the solution:

mass of solution = mass of water + mass of NaCl

The molar mass of NaCl is 58.44 g/mol.

mass of NaCl = moles of NaCl * molar mass of NaCl
mass of NaCl = 0.025 mol * 58.44 g/mol
mass of NaCl = 1.461 g

mass of solution = mass of water + mass of NaCl
mass of solution = 998.5056 g + 1.461 g
mass of solution ≈ 999.97 g

Now, we can calculate the percent by mass:

Percent by mass = (1.461 g / 999.97 g) * 100
Percent by mass ≈ 0.146%

Therefore, the concentration of the salt solution in percent by mass is approximately 0.146%.

D) To calculate the concentration of the salt solution in parts per million (ppm), we'll use the formula:

Concentration (ppm) = (mass of solute / mass of solution) * 1,000,000

Given:
Mass of solution = 999.97 g
Mass of NaCl = 1.461 g

Now, we can calculate the concentration in parts per million:

Concentration (ppm) = (1.461 g / 999.97 g) * 1,000,000
Concentration (ppm) ≈ 1461 ppm

Therefore, the concentration of the salt solution in parts per million is approximately 1461 ppm.

To calculate the answers to the questions, we'll need to use the given information and follow specific formulas for each calculation.

A) Calculation of molality:
Molality (m) is defined as the number of moles of solute per kilogram of solvent. To calculate it, we need to find the number of moles of NaCl and the mass of water.

Given:
Concentration of NaCl solution (C) = 2.500 × 10^(-2) M
Volume of water (V) = 999.3 mL = 0.9993 L
Density of water (ρ) = 0.9982 g/mL

We can use the formula:

Molarity (M) = moles of solute / liters of solution

Rearranging this equation:

Moles of solute = Molarity × liters of solution

Substituting the given values:

Moles of solute = (2.500 × 10^(-2) M) × 0.9993 L

Now, we need to convert the mass of water to kilograms:

Mass of water = volume of water × density of water
Mass of water = 0.9993 L × 0.9982 g/mL = 0.997 g

Finally, we can calculate the molality:

Molality (m) = moles of solute / mass of solvent in kg

Mass of solvent = mass of water in kg = 0.997 g ÷ 1000 = 0.997 kg

Now, we can substitute the values:

Molality = (2.500 × 10^(-2) M × 0.9993 L) / 0.997 kg

Solving this equation will give us the value of molality.

B) Calculation of mole fraction:
Mole fraction (χ) is defined as the ratio of the number of moles of one component to the total number of moles in the solution.

To calculate it, we need to find the number of moles of NaCl and the number of moles of water.

Number of moles of NaCl = Moles of solute (already calculated)

Number of moles of water = Mass of water / molar mass of water

The molar mass of water (H2O) is approximately (2 × atomic mass of hydrogen) + atomic mass of oxygen.

Now, we can calculate the mole fraction using the formula:

Mole fraction (χ) = Moles of solute / (Moles of solute + Moles of water)

Substituting the values will give us the mole fraction.

C) Calculation of concentration in percent by mass:
The concentration in percent by mass is the mass of solute divided by the mass of the solution, multiplied by 100.

To calculate this, we need to find the mass of NaCl and the mass of the solution.

Mass of NaCl = Moles of solute × molar mass of NaCl

Mass of solution = Mass of NaCl + Mass of water

Concentration in percent by mass = (Mass of NaCl / Mass of solution) × 100

Substituting the values will give the concentration in percent by mass.

D) Calculation of concentration in parts per million (ppm):
Parts per million (ppm) is a way to express concentration in very small amounts. It represents the ratio of the mass of solute to the mass of the solution, multiplied by 1,000,000.

To calculate this, we need to find the mass of NaCl and the mass of the solution.

Concentration in ppm = (Mass of NaCl / Mass of solution) × 10^6

Substituting the values will give the concentration in ppm.

By following these steps, you can calculate the answers to each question.

You must know how to do parts of this. What about the problem do you not understand?

a. m = mols/kg solvent. You have volume and density. That's how you determine kg solvent.

b. XNaCl = n/total mols
XH2O - n/total mols

c. % NaCl w/w = grams NaCl/100 g solution.

d. Take the answer from c (which is parts per hundred) and multiply by 10,000.