A 2.74-g sample of a substance suspected of being pure gold is warmed to 72.1 °C and submerged into 15.2 g of water initially at 24.7 °C. The final temperature of the mixture is 26.3 °C. What is the heat capacity of the unknown substance? Could the substance be pure gold?

Verified step by step guidance

1. Identify the known values: mass of the substance (m_1 = 2.74 \text{ g}), initial temperature of the substance (T_{i1} = 72.1 \text{ °C}), mass of water (m_2 = 15.2 \text{ g}), initial temperature of water (T_{i2} = 24.7 \text{ °C}), and final temperature of the mixture (T_f = 26.3 \text{ °C}).
2. Use the formula for heat transfer: q = mc\Delta T, where q is the heat absorbed or released, m is the mass, c is the specific heat capacity, and \Delta T is the change in temperature.
3. Calculate the heat gained by the water: q_{water} = m_2 \cdot c_{water} \cdot (T_f - T_{i2}), where c_{water} = 4.18 \text{ J/g°C}.
4. Assume no heat is lost to the surroundings, so the heat lost by the substance is equal to the heat gained by the water: q_{substance} = -q_{water}.
5. Calculate the specific heat capacity of the substance: c_{substance} = \frac{-q_{water}}{m_1 \cdot (T_f - T_{i1})}. Compare this value to the known specific heat capacity of gold (0.129 \text{ J/g°C}) to determine if the substance could be pure gold.