Question

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What is the molar concentration and percent by mass of a 25.00 mL aqueous copper (II) sulfate solution if the mass of copper (II) sulfate is 12.50 g and the density of this solution is 1.005 g/mL?

Answer 1

First, we need to calculate the molar concentration of the copper (II) sulfate solution. We can use the formula:

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

To find the moles of copper (II) sulfate, we need to divide the given mass by its molar mass. The molar mass of copper (II) sulfate is:

CuSO4 = 63.55 g/mol (for copper) + 32.07 g/mol (for sulfur) + 4 x 16.00 g/mol (for oxygen)
CuSO4 = 159.61 g/mol

So, the moles of copper (II) sulfate are:

moles of CuSO4 = 12.50 g / 159.61 g/mol = 0.0783 mol

Next, we need to calculate the volume of the solution. We are given the density of the solution, so we can use the formula:

density = mass / volume

Solving for volume, we get:

volume of solution = mass / density = 12.50 g / 1.005 g/mL = 12.438 mL

Note that we used 12.438 mL instead of 25.00 mL because the density of the solution is less than 1 g/mL, which means that a given volume of the solution has less mass than the same volume of pure water.

Now that we have the volume of the solution, we can convert it to liters and calculate the molarity:

molarity = 0.0783 mol / 0.012438 L = 6.29 M

Next, we need to calculate the percent by mass of copper (II) sulfate in the solution. This is given by the formula:

percent by mass = (mass of solute / mass of solution) x 100%

The mass of the solution is the mass of copper (II) sulfate plus the mass of water. We can calculate the mass of water by subtracting the mass of copper (II) sulfate from the total mass:

mass of water = mass of solution - mass of CuSO4 = 12.50 g / 1.005 g/mL - 12.50 g = 0.0622 g

So, the mass of the solution is:

mass of solution = 12.50 g + 0.0622 g = 12.5622 g

Therefore, the percent by mass of copper (II) sulfate in the solution is:

percent by mass = (12.50 g / 12.5622 g) x 100% = 99.5% (rounded to one decimal place)

Therefore, the molar concentration of the copper (II) sulfate solution is 6.29 M and the percent by mass of copper (II) sulfate in the solution is 99.5%.

Answer 2

The percent by mass of the solution is 49.677%.

Step-by-step explanation:

First, we need to find the molar concentration of the solution:

Calculate the number of moles of copper (II) sulfate in the solution:

m = 12.50 g

M = 159.609 g/mol (molar mass of copper (II) sulfate)

n = m/M = 0.0783 mol

Calculate the volume of the solution in liters:

V = 25.00 mL = 0.025 L

Calculate the molar concentration:

C = n/V = 0.0783 mol/0.025 L = 3.132 M

The molar concentration of the solution is 3.132 M.

Next, we can find the percent by mass of the solution:

Calculate the mass of the solution:

m_solution = V × ρ = 0.025 L × 1.005 g/mL = 0.025125 g

Calculate the percent by mass:

% by mass = (m_copper sulfate / m_solution) × 100%

= (12.50 g / 25.125 g) × 100%

= 49.677%

The percent by mass of the solution is 49.677%.