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Chapter 6: Problem 56

The specific heat capacity of silver is 0.24 $\mathrm{J} /^{\circ} \mathrm{C} \cdot \mathrm{g}$ a. Calculate the energy required to raise the temperature of 150.0 g Ag from 273 \(\mathrm{K}\) to 298 \(\mathrm{K}\) . b. Calculate the energy required to raise the temperature of 1.0 mole of \(\mathrm{Ag}\) by \(1.0^{\circ} \mathrm{C}\) (called the molar heat capacity of silver). c. It takes 1.25 \(\mathrm{kJ}\) of energy to heat a sample of pure silver from \(12.0^{\circ} \mathrm{C}\) to \(15.2^{\circ} \mathrm{C}\) . Calculate the mass of the sample of silver.

Short Answer

Expert verified
The energy required to raise the temperature of 150.0 g Ag from 273 K to 298 K is 900 J, the energy required to raise the temperature of 1.0 mole of Ag by 1.0°C is 25.89 J, and the mass of the sample of silver that takes 1.25 kJ of energy to heat from 12.0°C to 15.2°C is approximately 1625 g.

Step by step solution

01

a. Calculate the energy required to raise the temperature of 150.0 g Ag from 273 K to 298 K.

First, we need to convert the temperature from Kelvins to Celsius: 273 K = 0°C and 298 K = 25°C. Now use the formula Q = mcΔT: Mass (m) = 150.0 g Specific heat capacity (c) = 0.24 J/(g°C) Change in temperature (ΔT) = 25°C - 0°C = 25°C Q = (150.0 g) * (0.24 J/(g°C)) * (25°C) Q = 900 J The energy required to raise the temperature of 150.0 g Ag from 273 K to 298 K is 900 J.
02

b. Calculate the energy required to raise the temperature of 1.0 mole of Ag by 1.0°C.

First, we have to calculate the mass of 1.0 mole of Ag: Molar mass of Ag = 107.87 g/mol Mass (m) = (1.0 mol) * (107.87 g/mol) = 107.87 g Now, use the formula Q = mcΔT with ΔT = 1.0°C: Q = (107.87 g) * (0.24 J/(g°C)) * (1.0°C) Q = 25.89 J The energy required to raise the temperature of 1.0 mole of Ag by 1.0°C is 25.89 J.
03

c. It takes 1.25 kJ of energy to heat a sample of pure silver from 12.0°C to 15.2°C. Calculate the mass of the sample of silver.

First, we need to convert the energy from kJ to J: 1.25 kJ * 1000 = 1250 J Now we have the energy (Q), the specific heat capacity (c), and the change in temperature (ΔT = 15.2°C - 12.0°C). We can rewrite the formula Q = mcΔT to solve for mass (m): m = Q / (c * ΔT) m = (1250 J) / (0.24 J/(g°C) * (15.2°C - 12.0°C)) m = 1250 J / (0.24 J/(g°C) * 3.2°C) m ≈ 1625 g The mass of the sample of silver is approximately 1625 g.

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