Question

heptane and water do not mix, and heptane has a lower density (0.684 g/ml) than water (1.00 g/ml). a 100 - ml graduated cylinder with an inside diameter of 3.20 cm contains 35.8 g of heptane and 30.7 g of water. what is the combined height of the two liquid layers in the cylinder? the volume of a cylinder is $pi r^{2}h$, where r is the radius and h is the height.

Explanation:

Step1: Calculate volume of heptane

Use density formula $
ho=\frac{m}{V}$, so $V_{heptane}=\frac{m_{heptane}}{
ho_{heptane}}$. Given $m_{heptane} = 35.8\ g$ and $
ho_{heptane}=0.684\ g/mL$, then $V_{heptane}=\frac{35.8}{0.684}\ mL\approx52.34\ mL$.

Step2: Calculate volume of water

Using density formula $
ho=\frac{m}{V}$, so $V_{water}=\frac{m_{water}}{
ho_{water}}$. Given $m_{water} = 30.7\ g$ and $
ho_{water}=1.00\ g/mL$, then $V_{water}=\frac{30.7}{1.00}\ mL = 30.7\ mL$.

Step3: Calculate total volume

$V_{total}=V_{heptane}+V_{water}=52.34 + 30.7=83.04\ mL$. Since $1\ mL = 1\ cm^{3}$, $V_{total}=83.04\ cm^{3}$.

Step4: Calculate radius of cylinder

Given diameter $d = 3.20\ cm$, radius $r=\frac{d}{2}=\frac{3.20}{2}=1.60\ cm$.

Step5: Calculate height of liquid layers

From volume formula of cylinder $V=\pi r^{2}h$, we can solve for $h$. So $h=\frac{V}{\pi r^{2}}$. Substitute $V = 83.04\ cm^{3}$ and $r = 1.60\ cm$ into the formula: $h=\frac{83.04}{\pi\times(1.60)^{2}}=\frac{83.04}{3.14\times2.56}\ cm\approx10.2\ cm$.

Answer:

$10.2$