Question

determine the volume, in ml, of a 381.9 - g sample of an alloy with density of 0.258 $\frac{lb}{in^{3}}$.
0.217ml
53.5ml
3.26ml
8.28ml

8 multiple choice 10 points
glycerol is an extremely viscous solution, density of 1.26 g/cm³, that is usually measured by weight. how many grams of glycerol are requires for a reaction the calls for 9.30 ml of glycerol.
0.135g
135g
11.700g
11.7g

Explanation:

Step1: Recall density formula

The density formula is $
ho=\frac{m}{V}$, where $
ho$ is density, $m$ is mass and $V$ is volume. We can re - arrange it to $V = \frac{m}{
ho}$ for the first problem and $m=
ho V$ for the second problem. Also, note that $1\ cm^{3}=1\ mL$.

Step2: Solve for the volume of the alloy

Given $m = 381.9\ g$ and $
ho=0.258\frac{lb}{in^{3}}$. First, convert the density to $g/cm^{3}$. Since $1\ lb = 453.592\ g$ and $1\ in^{3}=16.3871\ cm^{3}$, then $
ho=0.258\frac{453.592\ g}{16.3871\ cm^{3}}\approx7.14\ g/cm^{3}$. Then $V=\frac{m}{
ho}=\frac{381.9\ g}{7.14\ g/cm^{3}}\approx53.5\ cm^{3}=53.5\ mL$.

Step3: Solve for the mass of glycerol

Given $
ho = 1.26\ g/cm^{3}$ and $V = 9.30\ mL=9.30\ cm^{3}$. Using $m=
ho V$, we have $m=1.26\ g/cm^{3}\times9.30\ cm^{3}=11.718\ g\approx11.7\ g$.

Answer:

1. 53.5mL
2. 11.7g