Question

(a) Calculate the molarity of a solution made by dissolving \(0.750\) grams of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) in enough water to form exactly \(850 \mathrm{~mL}\) of solution. (b) How many moles of \(\mathrm{KMnO}_{4}\) are present in \(250 \mathrm{~mL}\) of a \(0.0475 \mathrm{M}\) solution? (c) How many milliliters of \(11.6 \mathrm{M} \mathrm{HCl}\) solution are needed to obtain \(0.250 \mathrm{~mol}\) of \(\mathrm{HCl}\) ?

Short answer

(a) The molarity of the Na2SO4 solution is \(6.21 \times 10^{-3}\:M\). (b) There are 0.0119 moles of KMnO4 in 250 mL of a 0.0475 M solution. (c) We need 21.6 mL of an 11.6 M HCl solution to obtain 0.250 mol of HCl.

Step-by-step solution

1. Determine the moles of Na2SO4 in the solution

First, we need to find the molar mass of Na2SO4. Na has a molar mass of 22.99g/mol, S is 32.07g/mol, and O is 16.00g/mol. Therefore, the molar mass of Na2SO4 is \(2(22.99) + 1(32.07) + 4(16.00)= 142.04g/mol\) Now we can determine the moles of Na2SO4 in the solution: Moles of Na2SO4 = \(\frac{0.750\:g}{142.04\:g/mol}\) Moles of Na2SO4 = \(5.285 \times 10^{-3}\) mol

2. Calculate the solution volume in liters

We are given the solution volume in milliliters, so we need to convert it to liters: Volume = \(\frac{850\:mL}{1000\:mL/L}\) = 0.850 L

3. Calculate the molarity of the solution

Now we can calculate the molarity using the formula mentioned earlier: Molarity (M) = \(\frac{5.285 \times 10^{-3}\:mol}{0.850\:L}\) = \(6.21 \times 10^{-3}\:M\) The molarity of the Na2SO4 solution is \(6.21 \times 10^{-3}\:M\). (b) Find the moles of KMnO4 in the solution

1. Calculate the moles of KMnO4 in the solution

We are given the molarity and volume of the solution, so we can use the molarity formula to find the moles: Moles of KMnO4 = Molarity x Volume = \(0.0475 \mathrm{M}\) x \(\frac{250\:mL}{1000\:mL/L}\) = 0.0119 mol There are 0.0119 moles of KMnO4 in 250 mL of a 0.0475 M solution. (c) Determine the volume of the 11.6 M HCl solution required for 0.250 mol of HCl

1. Calculate the volume of the HCl solution needed

Again, using the molarity formula and the given molarity and moles, we can find the volume: Volume = \(\frac{0.250\:mol}{11.6\:M}\) = 0.0216 L

2. Convert the volume to milliliters

Lastly, we convert the volume in liters to milliliters: Volume = \(0.0216\:L \times \frac{1000\:mL}{1\:L}\) = 21.6 mL We need 21.6 mL of an 11.6 M HCl solution to obtain 0.250 mol of HCl.