How much heat is required to heat 19 g of solid silver from 100 ◦C to liquid silver at 961◦C? The specific heat of solid silver is 0.235 J/g ·◦ C, and the heat of fusion of silver at its melting point of 961◦C is 11.3 kJ/g.
Answer in units of kJ
To calculate the heat required to heat the solid silver from 100°C to its melting point at 961°C and then melt it, we need to consider two steps: heating the solid silver and then melting it.
Step 1: Heating the solid silver from 100°C to its melting point:
The specific heat capacity of solid silver is given as 0.235 J/g·°C.
The change in temperature is (961°C - 100°C) = 861°C.
The mass of solid silver is 19 g.
The heat required to heat the solid silver can be calculated using the formula:
Q = m * c * ΔT
Q = 19 g * 0.235 J/g·°C * 861°C
Q = 3764.665 J
Converting J to kJ:
Q = 3764.665 J / 1000
Q = 3.764665 kJ
Step 2: Melting the solid silver:
The heat of fusion of silver is given as 11.3 kJ/g.
The mass of solid silver is 19 g.
The heat required to melt the solid silver can be calculated using the formula:
Q = m * ΔHf
Q = 19 g * 11.3 kJ/g
Q = 214.7 kJ
Therefore, the total heat required to heat 19 g of solid silver from 100°C to liquid silver at 961°C is:
Total Q = Q1 + Q2 = 3.764665 kJ + 214.7 kJ
Total Q = 218.464665 kJ
Hence, the heat required is approximately 218.46 kJ.
To calculate the total heat required to heat solid silver from 100°C to its melting point at 961°C, we need to consider two separate processes:
1. Heating the solid silver from 100°C to its melting point:
Since the specific heat of solid silver is given as 0.235 J/g·°C, we can use the formula: q = m * c * ΔT.
Here:
q = heat energy
m = mass of the solid silver = 19 g
c = specific heat of solid silver = 0.235 J/g·°C
ΔT = change in temperature = (961°C - 100°C)
Calculating q1:
q1 = (19 g) * (0.235 J/g·°C) * (961°C - 100°C)
= 19 * 0.235 * 861
≈ 387.36 J
2. Melting the solid silver at its melting point:
The heat of fusion of silver at its melting point is given as 11.3 kJ/g. Here, we need to convert grams to kilograms to be consistent with the units used for the heat of fusion.
Calculating q2:
q2 = (19 g) * (11.3 kJ/g)
= 19 * 11.3
= 215.7 kJ
To get the total heat required, we add q1 and q2:
Total heat = q1 + q2
= 387.36 J + 215.7 kJ
= 215.7 kJ + 0.38736 kJ
≈ 216.08736 kJ
Therefore, the total heat required to heat 19 g of solid silver from 100°C to liquid silver at 961°C is approximately 216.08736 kJ.
q1 = heat to raise T from 19 C to 961 C.
q1 = mass Ag x specific heat Ag x (Tfinal-Tnitial)
q2 = heat to melt Ag.
q2 = mass Ag x heat fusion
Total q = q1 + q2