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Chapter 6: Problem 50

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 \(150.0 \mathrm{~g}\) Ag from \(273 \mathrm{~K}\) to \(298 \mathrm{~K}\). b. Calculate the energy required to raise the temperature of \(1.0 \mathrm{~mol} \mathrm{Ag}\) 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
a. The energy required to raise the temperature of 150.0 g Ag from 273 K to 298 K is 900 J. b. The molar heat capacity of silver is 25.89 J/mol·°C. c. The mass of the silver sample is 16250.0 g.

Step by step solution

01

Identify the given information and formula

The given information is: Specific heat capacity of silver (c) = 0.24 J/°C·g, Mass of silver (m) = 150.0 g, Initial temperature (T₁) = 273 K, Final temperature (T₂) = 298 K To calculate the energy required, use the formula: Energy (Q) = mc(T₂ - T₁)
02

Calculate the energy required

Substitute the given values into the formula: Q = (150.0 g) (0.24 J/°C·g) (298 K - 273 K) Q = (150.0 g) (0.24 J/°C·g) (25 K) Q = 900 J The energy required to raise the temperature of 150.0 g Ag from 273 K to 298 K is 900 J. b. Calculate the energy required to raise the temperature of 1.0 mol Ag by 1.0°C (called the molar heat capacity of silver).
03

Identify the given information and formula

The given information is: Specific heat capacity of silver (c) = 0.24 J/°C·g, Molar mass of silver (M) = 107.87 g/mol To calculate the molar heat capacity, use the formula: Molar heat capacity = c × M
04

Calculate the molar heat capacity

Substitute the given values into the formula: Molar heat capacity = (0.24 J/°C·g) (107.87 g/mol) Molar heat capacity = 25.89 J/mol·°C The molar heat capacity of silver is 25.89 J/mol·°C. 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.
05

Identify the given information and formula

The given information is: Specific heat capacity of silver (c) = 0.24 J/°C·g, Initial temperature (T₁) = 12.0°C, Final temperature (T₂) = 15.2°C, Energy (Q) = 1.25 kJ = 1250 J To calculate the mass of the silver sample, use the formula: Mass (m) = Q / (c × (T₂ - T₁))
06

Calculate the mass of the silver sample

Substitute the given values into the formula: m = 1250 J / [(0.24 J/°C·g)(15.2°C-12.0°C)] m = 1250 J / [(0.24 J/°C·g)(3.2°C)] m = 16250.0 g The mass of the silver sample is 16250.0 g.

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Most popular questions from this chapter

The bombardier beetle uses an explosive discharge as a defensive measure. The chemical reaction involved is the oxidation of hydroquinone by hydrogen peroxide to produce quinone and water: $$ \mathrm{C}_{6} \mathrm{H}_{4}(\mathrm{OH})_{2}(a q)+\mathrm{H}_{2} \mathrm{O}_{2}(a q) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{4} \mathrm{O}_{2}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) $$ Calculate \(\Delta H\) for this reaction from the following data: \(\mathrm{C}_{6} \mathrm{H}_{4}(\mathrm{OH})_{2}(a q) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{4} \mathrm{O}_{2}(a q)+\mathrm{H}_{2}(g)\) $$ \begin{aligned} \Delta H &=+177.4 \mathrm{~kJ} \\ \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}_{2}(a q) & \Delta H=-191.2 \mathrm{~kJ} \\ \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g) & \Delta H=-241.8 \mathrm{~kJ} \\ \mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l) & \Delta H=-43.8 \mathrm{~kJ} \end{aligned} $$

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