Given that the density of water is approximately 1.00 g/cm^3, what is the mass in kilograms of 30 gallons of water? (1 gallon = 3.785 liters)

• A. 113.6 kg
• B. 30.0 kg
• C. 75.7 kg
• D. 227.2 kg

Answer: (A)

Verified step by step guidance

1. Start by converting the volume from gallons to liters using the given conversion factor: \$1 \text{ gallon} = 3.785 \text{ liters}\(. Multiply the volume in gallons by this factor to get the volume in liters: \)V_{\text{liters}} = 30 \times 3.785$.
2. Next, convert the volume from liters to cubic centimeters (cm³) because the density is given in g/cm³. Recall that \$1 \text{ liter} = 1000 \text{ cm}^3\(. So, multiply the volume in liters by 1000 to get the volume in cm³: \)V_{\text{cm}^3} = V_{\text{liters}} \times 1000$.
3. Use the density of water to find the mass in grams. Since density \(\rho = \frac{\text{mass}}{\text{volume}}\), rearrange to find mass: \(m = \rho \times V\). Here, \(\rho = 1.00 \text{ g/cm}^3\), so \(m = 1.00 \times V_{\text{cm}^3}\) grams.
4. Convert the mass from grams to kilograms by dividing by 1000, since \$1000 \text{ g} = 1 \text{ kg}\(. So, \)m_{\text{kg}} = \frac{m}{1000}$.
5. Summarize the calculation: \(m_{\text{kg}} = \frac{1.00 \times (30 \times 3.785 \times 1000)}{1000}\). Simplify the expression to find the mass in kilograms.