Problem: A solution is prepared by mixing 25 mL pentane (C5H12, d = 0.63 g/cm3) with 45 mL hexane (C6H14, d = 0.66 g/cm3). Assuming that the volumes add on mixing, calculate the mass percent, mole fraction, molality, and molarity of the pentane.

We are asked to calculate the mass percent, mole fraction, molality, and molarity of the pentane.

Step 1. Calculate mass of each

Recall: 

$$\begin{gathered} \boxed{\mathbf{density}\mathbf{ }\mathbf{=}\mathbf{ }\frac{\mathbf{mass}}{\mathbf{volume}}} \\ \mathbf{mass}\mathbf{ }{\mathbf{C}}_{\mathbf{5}}{\mathbf{H}}_{\mathbf{12}}\mathbf{ }\mathbf{=}\mathbf{25}\mathbf{ }\cancel{\mathbf{mL}}\mathbf{ }\mathbf{\times }\mathbf{ }\frac{\mathbf{1}\mathbf{ }\cancel{{\mathbf{cm}}^{\mathbf{3}}}}{\mathbf{1}\mathbf{ }\mathbf{ }\cancel{\mathbf{mL}}\mathbf{ }}\mathbf{\times }\frac{\mathbf{0}\mathbf{.}\mathbf{63}\mathbf{ }\mathbf{g}}{\mathbf{1}\mathbf{ }\cancel{{\mathbf{cm}}^{\mathbf{3}}}}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{15}\mathbf{.}\mathbf{75}\mathbf{ }\mathbf{g} \\ \mathbf{mass}\mathbf{ }{\mathbf{C}}_{\mathbf{6}}{\mathbf{H}}_{\mathbf{14}}\mathbf{ }\mathbf{=}\mathbf{45}\mathbf{ }\cancel{\mathbf{mL}}\mathbf{ }\mathbf{\times }\mathbf{ }\frac{\mathbf{1}\mathbf{ }\cancel{{\mathbf{cm}}^{\mathbf{3}}}}{\mathbf{1}\mathbf{ }\mathbf{ }\cancel{\mathbf{mL}}\mathbf{ }}\mathbf{\times }\frac{\mathbf{0}\mathbf{.}\mathbf{66}\mathbf{ }\mathbf{g}}{\mathbf{1}\mathbf{ }\cancel{{\mathbf{cm}}^{\mathbf{3}}}}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{29}\mathbf{.}\mathbf{7}\mathbf{ }\mathbf{g} \end{gathered}$$

Step 2. Calculate moles each

Molar mass C₅H₁₂ = 72.17 g/mol

Molar mass C₆H₁₄ = 86.20 g/mol

$$\begin{gathered} \mathbf{15}\mathbf{.}\mathbf{75}\cancel{\mathbf{ }\mathbf{g}\mathbf{ }{\mathbf{C}}_{\mathbf{5}}{\mathbf{H}}_{\mathbf{12}\mathbf{ }}}\mathbf{ }\mathbf{\times }\mathbf{ }\frac{\mathbf{1}\mathbf{ }\mathbf{mol}\mathbf{ }{\mathbf{C}}_{\mathbf{5}}{\mathbf{H}}_{\mathbf{12}\mathbf{ }}}{\mathbf{72}\mathbf{.}\mathbf{17}\mathbf{ }\cancel{\mathbf{ }\mathbf{g}\mathbf{ }{\mathbf{C}}_{\mathbf{5}}{\mathbf{H}}_{\mathbf{12}\mathbf{ }}}\mathbf{ }}\mathbf{=}\mathbf{ }\mathbf{0}\mathbf{.}\mathbf{22}\mathbf{ }\mathbf{ }\mathbf{mol}\mathbf{ }{\mathbf{C}}_{\mathbf{5}}{\mathbf{H}}_{\mathbf{12}\mathbf{ }} \\ \mathbf{29}\mathbf{.}\mathbf{7}\cancel{\mathbf{ }\mathbf{g}\mathbf{ }{\mathbf{C}}_{\mathbf{6}}{\mathbf{H}}_{\mathbf{14}\mathbf{ }}}\mathbf{ }\mathbf{\times }\mathbf{ }\frac{\mathbf{1}\mathbf{ }\mathbf{mol}\mathbf{ }{\mathbf{C}}_{\mathbf{6}}{\mathbf{H}}_{\mathbf{14}\mathbf{ }}}{\mathbf{76}\mathbf{.}\mathbf{20}\mathbf{ }\cancel{\mathbf{ }\mathbf{g}\mathbf{ }{\mathbf{C}}_{\mathbf{6}}{\mathbf{H}}_{\mathbf{14}\mathbf{ }}}\mathbf{ }\mathbf{ }}\mathbf{=}\mathbf{ }\mathbf{0}\mathbf{.}\mathbf{39}\mathbf{ }\mathbf{mol}\mathbf{ }{\mathbf{C}}_{\mathbf{6}}{\mathbf{H}}_{\mathbf{14}\mathbf{ }} \end{gathered}$$

Step 3. Mass percent pentane

$$\begin{gathered} \boxed{\mathbf{Mass}\mathbf{ }\mathbf{\%}\mathbf{ }\mathbf{=}\mathbf{ }\frac{\mathbf{mass}\mathbf{ }\mathbf{solute}}{\mathbf{mass}\mathbf{ }\mathbf{solution}}\mathbf{ }\mathbf{\times }\mathbf{100}} \\ \mathbf{Mass}\mathbf{ }\mathbf{\%}\mathbf{ }{\mathbf{C}}_{\mathbf{5}}{\mathbf{H}}_{\mathbf{12}}\mathbf{=}\mathbf{ }\frac{\mathbf{15}\mathbf{.}\mathbf{75}\mathbf{ }\mathbf{g}}{\mathbf{15}\mathbf{.}\mathbf{75}\mathbf{ }\mathbf{g}\mathbf{+}\mathbf{ }\mathbf{29}\mathbf{.}\mathbf{7}\mathbf{ }\mathbf{g}}\mathbf{ }\mathbf{\times }\mathbf{100} \\ \mathbf{Mass}\mathbf{ }\mathbf{\%}\mathbf{ }{\mathbf{C}}_{\mathbf{5}}{\mathbf{H}}_{\mathbf{12}}\mathbf{=}\mathbf{ }\frac{\mathbf{15}\mathbf{.}\mathbf{75}\mathbf{ }\cancel{\mathbf{g}}}{\mathbf{45}\mathbf{.}\mathbf{45}\mathbf{ }\cancel{\mathbf{g}}}\mathbf{ }\mathbf{\times }\mathbf{100} \end{gathered}$$

Mass % C₅H₁₂ = 34.65 %