When 200 cm^3 of liquid water freezes to form ice, what is the approximate volume of the resulting ice? (Assume the density of water is 1.00 g/cm^3 and the density of ice is 0.92 g/cm^3.)

• A. 184 cm^3
• B. 200 cm^3
• C. 92 cm^3
• D. 217 cm^3

Answer: (D)

Verified step by step guidance

1. Identify the given data: initial volume of liquid water \(V_{water} = 200\ \text{cm}^3\), density of water \(\rho_{water} = 1.00\ \text{g/cm}^3\), and density of ice \(\rho_{ice} = 0.92\ \text{g/cm}^3\).
2. Calculate the mass of the water before freezing using the formula \(m = \rho \times V\). Since density of water is \$1.00\ \text{g/cm}^3\(, the mass is \)m = 1.00 \times 200 = 200\ \text{g}$.
3. Recognize that mass remains constant during the phase change from water to ice, so the mass of ice is also \$200\ \text{g}$.
4. Use the density of ice to find the volume of ice formed by rearranging the density formula: \(V = \frac{m}{\rho}\). Substitute \(m = 200\ \text{g}\) and \(\rho_{ice} = 0.92\ \text{g/cm}^3\) to get \(V_{ice} = \frac{200}{0.92}\).
5. Interpret the result: since the density of ice is less than that of water, the volume of ice will be greater than the original volume of water, which explains why ice expands upon freezing.