Answer to Question #172529 in General Chemistry for Blank 0822

Question

40.0 grams of Calcium Carbonate compound (CaCO3) with molar mass of 100g/mole, in order to make an aqueous solution that has a mole fraction of solute of 0.200? How much H2O is needed to achieved the desired result? 

Answer 1

Q172529

40.0 grams of Calcium Carbonate compound (CaCO₃) with a molar mass of 100g/mole, in order to make an aqueous solution that has a mole fraction of solute of 0.200? How much H2O is needed to achieve the desired result? 

Solution:

We will first convert 40.0 g of CaCO₃ to moles by using the molar mass 100 g/mole.

Here CaCO₃ is the solute and H₂O is the solvent.

By using the moles of CaCO₃ and the given mole fraction of solute (CaCO₃) we can find the total moles in the solution.

Next from the total moles and moles of CaCO₃, we can find the moles of solvent (water ).

Lastly, we can convert moles of H₂O to grams of H₂O.

Step 1: Convert 40.0 grams of CaCO₃ to moles by using the molar mass 100 g/mole.

$$moles \space of \space CaCO_3 = 40.0g \space of\space CaCO_3 * \frac{ 1\space mol \space CaCO_3 }{100 \space g \space CaCO_3 }$$

$$= 0.40\space mol\space of \space CaCO_3$$

Step 2: To find total moles in solution by using 0.40 mol CaCO₃ and

mole fraction of solute CaCO₃ = 0.200.

$$mole \space fraction \space of \space CaCO_3 = \frac{moles \space of \space CaCO_3 }{ total \space moles \space in \space solution }$$

Arranging this equation for Total moles, we have

$$total \space moles \space in \space solution = \frac{moles \space of \space CaCO_3 }{mole \space fraction \space of \space CaCO_3 }$$

$$= \frac{0.40\space mol }{0.20 } = 2.00 moles$$

Hence total moles of solute and solvent in the solution is 2.00 moles.

Step 3: To find moles of H₂O (solvent)

moles of solution = moles of solute ( CaCO₃ ) + moles of solvent ( H₂O).

Substitute moles of solution = 2.00 moles, and moles of solute = 0.40 moles, we have

2.00 mol = 0.40 mol + moles of solvent ( H₂O).

moles of solvent ( H₂O) = 2.00 mol - 0.40 mol = 1.60 moles.

Hence moles of solvent ( water ) in the solution is 1.60 moles.

Step 4: To convert moles of H₂O to grams by using its molar mass.

molar mass of H2O = 2 * atomic mass of H + 1 * atomic mass of O

= 2 * 1.00794 g/mol + 1 * 15.999 g/mol

= 2.01588 g/mol + 15.999 g/mol

= 18.015 g/mol.

$$grams\space of \space H_2O = 1.60\space mol \space H_2O * \frac{18.015\space g \space of\space H_2O }{1\space mol\space of\space H_2O }$$

$$= 28.824\space grams \space of\space H_2O$$

in the given question we are given all the quantities in 3 significant figure, so our final answer must also be in 3 significant figure.

So the mass of water required to achieve the desired result is 28.8 grams.