Answer :
Final answer:
The heat needed to raise the temperature of a 2.6g piece of gold from 25°C to its melting point is 346.782 J. Without the heat of fusion for gold, we cannot calculate the total heat needed to melt it. Therefore, we can't determine the correct choice from the given options as they are incomplete without this additional data.
Explanation:
To calculate how much heat is needed to melt a 2.6 g piece of pure gold that is initially at 25 degrees Celsius, we need to know the specific heat of gold and its melting point. Gold has a melting point of 1,064 degrees Celsius and a specific heat of 0.129 J/g°C. First, we calculate the heat required to raise the temperature of gold from 25°C to the melting point of 1,064°C using the formula:
Q = m × c × ΔT
where Q is the heat energy, m is the mass, c is the specific heat, and ΔT is the change in temperature. For this piece of gold:
Q = 2.6 g × 0.129 J/g°C × (1,064°C - 25°C)
Q = 2.6 g × 0.129 J/g°C × 1,039°C
Q = 346.782 J
Then, we must add the heat required to actually melt the gold at its melting point. This requires the heat of fusion for gold, which is not provided in the question.
Since this additional information is not provided, we cannot accurately determine the total heat required to melt the gold without making assumptions. We can calculate the energy needed to raise the temperature but without the heat of fusion, selecting one of the provided options (A, B, C, D) would be speculative.
