The molar heats of fusion and vaporization for silver are 11.3 kJ/mol and 250. kJ/mol, respectively. Silver's normal melting point is 962°C, and its normal boiling point is 2212°C. What quantity of heat is required to melt 13.0 g of silver at 962°C?
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To calculate the quantity of heat required to melt 13.0 g of silver at 962°C, we need to use the heat equation:
Q = m * ΔHf
where:
Q = quantity of heat in joules (J)
m = mass of the substance in grams (g)
ΔHf = molar heat of fusion in J/mol
First, we need to convert the mass of silver from grams to moles using the molar mass of silver.
The molar mass of silver (Ag) is approximately 107.87 g/mol.
Number of moles of silver = mass of silver / molar mass of silver
Number of moles of silver = 13.0 g / 107.87 g/mol
Number of moles of silver ≈ 0.1204 mol
Next, we can calculate the quantity of heat required to melt 0.1204 mol of silver at its melting point.
Q = m * ΔHf
Q = 0.1204 mol * 11.3 kJ/mol
Since the molar heat of fusion is given in kJ/mol and we need the quantity of heat in joules, let's convert kilojoules (kJ) to joules (J) by multiplying by 1,000:
Q = 0.1204 mol * (11.3 kJ/mol * 1,000 J/1 kJ)
Q = 0.1204 mol * 11,300 J/mol
Finally, we can calculate the quantity of heat required:
Q = 0.1204 mol * 11,300 J/mol
Q ≈ 1,361 J
Therefore, approximately 1,361 joules of heat are required to melt 13.0 grams of silver at 962°C.
To find the quantity of heat required to melt 13.0 g of silver at 962°C, we can use the equation:
q = m * ΔH
Where:
q = quantity of heat (in joules)
m = mass of the substance (in grams)
ΔH = molar heat of fusion (in joules/gram)
First, we need to convert the mass of silver from grams to moles using its molar mass. The molar mass of silver (Ag) is 107.87 g/mol.
Mass of silver (m) = 13.0 g
Molar mass of silver (M) = 107.87 g/mol
Number of moles (n) = m / M
= 13.0 g / 107.87 g/mol
≈ 0.1204 mol
Now we can calculate the quantity of heat (q) required to melt the given amount of silver at its melting point.
q = m * ΔH
= n * ΔH
= 0.1204 mol * 11.3 kJ/mol (Note: Convert kJ to J)
= 0.1204 mol * 11,300 J/mol
≈ 1,360 J
Therefore, the quantity of heat required to melt 13.0 g of silver at 962°C is approximately 1,360 Joules.