Let's solve the two questions step by step.

Given Information:

• Density of acetone: $0.7857 \, \text{g/cm}^3$
• $1 \, \text{mL} = 1 \, \text{cm}^3$

Part A: Find the mass $m$ in grams of $12.30 \, \text{mL}$ of acetone.

The formula for mass is: $m = \text{density} \times \text{volume}$

Substitute the values: $m = 0.7857 \, \text{g/cm}^3 \times 12.30 \, \text{cm}^3$

$m = 9.662 \, \text{g}$

The answer, to four significant figures, is: $\boxed{9.662 \, \text{g}}$

Part B: Find the volume $V$ in mL of $9.52 \, \text{g}$ of acetone.

The formula for volume is: $V = \frac{\text{mass}}{\text{density}}$

Substitute the values: $V = \frac{9.52 \, \text{g}}{0.7857 \, \text{g/cm}^3}$

$V = 12.12 \, \text{cm}^3$

The answer, to three significant figures, is: $\boxed{12.1 \, \text{mL}}$

Would you like me to clarify any step or provide additional explanations?

Related Questions:

1. What is the physical significance of density in this calculation?
2. How can density be used to convert between mass and volume for other substances?
3. How do significant figures affect precision in scientific calculations?
4. What are the units of density and how are they derived?
5. How would you solve these questions if the volume were given in liters instead of milliliters?

Tip:

Always ensure the units are consistent (e.g., convert mL to cm³) when using formulas involving density, volume, and mass.