Question

How many grams of CaCl2

are needed to make 344.9
g of a solution that is 32.0
% (m/m) CaCl2
in water? Note that mass is not technically the same thing as weight, but % (m/m) has the same meaning as % (w/w).
grams CaCl2=


g

How many grams of water are needed to make this solution?
grams H2O=

Answer 1

`\boxed{\text{110.4 g of CaCl$_(2 )$ and 234.5 g of water}}`

Step-by-step explanation:

1. Mass of CaCl₂

`\text{Let m = mass of CaCl}_(2)\\\\\begin{array}{rcl}\text{Mass percent} & = & \frac{\text{Mass of CaCl}_(2)}{\text{Total mass}} * 100 \%\\\\32.0 \% & = & \frac{m}{\text{344.9 g}} * 100 \% \\\\\text{32.0 $*$ 344.9 g} & = & 100 m\\\\m & = &\frac{\text{32.0 $*$ 344.9 g}}{100}\\\\ & = &\textbf{110.4 g}\\\end{array}\\\text{You need $\boxed{\textbf{110.4 g}}$ of calcium chloride}`

2. Mass of water

`\text{Let m = mass of water}\\\begin{array}{rcl}\\\text{Mass of water + mass of CaCl}_(2) & = & \text{Mass of solution}\\m + 110.4 & = & 344.9\\m & = &\mathbf{234.5}\\\end{array}\\\text{The mass of water needed is $\boxed{\textbf{234.5 g}}$}`