Question

A solution is prepared with $70.0gofHN{O}_3$and $130.0gof{H}_{2}O$. The $HN{O}_3$solution has a density of $1.21g/mL$.

a. What is the mass percent role="math" localid="1652765432131" $(m/m)$of the $HN{O}_3$solution?

b. What is the total volume, in milliliters, of the solution?

c. What is the mass/volume percent $(m/v)$of the solution?

d. What is the molarity $\left(M\right)$of the solution?

Short answer

(Part a) The Mass percent$(m/m)$of the$HN{O}_3$solution is$35\%.$

(Part b) The Total Volume in milliliters of the solution is$163.5mL.$

(Part c) The mass/volume percent $(m/v)$of the solution is$42.34\%.$

(Part d) The Molarity of the solution is$6.72MHN{O}_3.$

Step-by-step solution

Introduction(Part a)

A mass percentage is a density of solute affirmation that can be approximated from the volume of the solution. The following formula expresses it:

$\text{Mass percentage of solute}=\frac{\text{grams of solute}}{\text{grams of solution}}\times 100\mathrm{\%}$

Given Information (part a).

Mass of Solute $\left(HN{O}_3\right)=70.0g$

Mass of Solvent $\left(H_{2}O\right)=130.0g$

Mass of Solution$(HN{O}_3+H_{2}O)=130.0g+70.0g=200g$

Explanation (part a).

Determine the Mass percentage:

$\text{Mass percentage of solute}=\frac{\text{grams of solute}}{\text{grams of solution}}\times 100\mathrm{\%}$

$$\begin{gathered} \text{Mass percent}=\left(\frac{70.0\mathrm{g}}{200.0\mathrm{g}}\right)\times 100\mathrm{\%} \\ =35\% \end{gathered}$$

Given Information (part b).

Mass of Solute$\left(HN{O}_3\right)=70.0g$

Mass of Solvent$\left(H_{2}O\right)=130.0g$

Mass of Solution$(HN{O}_3+H_{2}O)=130.0g+70.0g=200g$

Explanation (part b). 

Calculate the Total Volume in milliliters:

$\text{density}=\frac{\text{mass}\left(\mathrm{g}\right)}{\text{volume}\left(\mathrm{mL}\right)}$

$\mathrm{volume}\left(\mathrm{mL}\right)=\frac{\text{mass}\left(\mathrm{g}\right)}{\mathrm{density}}$

localid="1652769346930" $$\begin{gathered} \text{volume}\left(\mathrm{mL}\right)=\frac{200.0\mathrm{g}}{1.21\mathrm{g}{\mathrm{mL}}^{-1}} \\ =165.3mL \end{gathered}$$

Given Information (part c).

Mass of Solute $\left(HN{O}_3\right)=70.0g$

Volume of solution is$163.5mL.$

Explanation (part c). 

Find the mass/volume percent:

$\text{Mass percentin}\mathrm{m}/\mathrm{V}=\left(\frac{\text{mass of solute}}{\text{Volume of solution}}\right)\times 100\mathrm{\%}$

$$\begin{gathered} \text{Mass percent}=\left(\frac{70.0\mathrm{g}}{165.3\mathrm{mL}}\right)\times 100\mathrm{\%} \\ \mathrm{Mass}percent=42.34\% \end{gathered}$$

Given Information (part d).

Volume of Solution is $163.5mL$

convert it into Liters,

$$\begin{gathered} 1L=1000mL \\ =165.3m\mathrm{L}\times \frac{1.00\mathrm{L}}{1000m\mathrm{L}} \\ =0.1653\mathrm{mL} \end{gathered}$$

Explanation (part d). 

Find the Concentration of $HN{O}_3$:

$$\begin{gathered} \text{Concentration of}{\mathrm{HNO}}_3=\frac{\text{number of}\mathrm{mol}{\mathrm{HNO}}_3}{\text{volume in}\mathrm{L}} \\ =\frac{1.11\mathrm{mol}{\mathrm{HNO}}_3}{0.1653\mathrm{L}} \\ =6.72MHN{O}_3 \end{gathered}$$