How many grams of ethanol $\left( \text { density } 0.80 \mathrm {~g} / \mathrm { cm } ^ { 3 } \right)$ should be added to 5.0 g of chloroform (density $\left. 1.5 \mathrm {~g} / \mathrm { cm } ^ { 3 } \right)$ if the resulting mixture is to have a density of $1.2 \mathrm {~g} / \mathrm { cm } ^ { 3 } ?$ Assume that the fluids do not change their volumes when they are mixed.
A) 1.8 g
B) 1.6 g
C) 2.4 g
D) 2.0 g
E) 4.4 g

Question

How many grams of ethanol $\left( \text { density } 0.80 \mathrm {~g} / \mathrm { cm } ^ { 3 } \right)$ should be added to 5.0 g of chloroform (density $\left. 1.5 \mathrm {~g} / \mathrm { cm } ^ { 3 } \right)$ if the resulting mixture is to have a density of $1.2 \mathrm {~g} / \mathrm { cm } ^ { 3 } ?$ Assume that the fluids do not  change their volumes when they are mixed.
A) 1.8 g
B) 1.6 g
C) 2.4 g
D) 2.0 g
E) 4.4 g

Quizplus · Accepted Answer

To find the mass of ethanol needed, we can use the formula for the final density of a mixture: $\text{density}_{\text{final}} = \frac{\text{mass}_{\text{total}}}{\text{volume}_{\text{total}}}$. Given the densities of ethanol and chloroform, and their masses, we can calculate their volumes ($\text{volume} = \frac{\text{mass}}{\text{density}}$). For chloroform, $\text{volume} = \frac{5.0 \, \text{g}}{1.5 \, \text{g/cm}^3} = 3.33 \, \text{cm}^3$. Let $x$ be the mass of ethanol added, so its volume is $\frac{x}{0.80 \, \text{g/cm}^3}$. The total mass is $5.0 \, \text{g} + x$, and the total volume is $3.33 \, \text{cm}^3 + \frac{x}{0.80}$. Setting the final density to $1.2 \, \text{g/cm}^3$, we solve for $x$: $1.2 = \frac{5.0 + x}{3.33 + \frac{x}{0.80}}$. Solving this equation gives $x = 2.0 \, \text{g}$.

How Many Grams of Ethanol ( density 0.80 g/cm3)\left( \text { density } 0.80 \mathrm {~g} / \mathrm { cm } ^ { 3 } \right)( density 0.80 g/cm3)

How Many Grams of Ethanol $\left( \text { density } 0.80 \mathrm {~g} / \mathrm { cm } ^ { 3 } \right)$