At 1 atm, how much energy is required to heat 39.0 g of H2O(s) at –22.0 °C to H2O(g) at 163.0 °C?
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To calculate the energy required to heat a substance, we need to use the specific heat capacity and the change in temperature. In this case, we need to calculate the energy required to heat solid water (H2O(s)) to gaseous water (H2O(g)).
Here are the steps to calculate the energy required:
1. Calculate the energy required to heat the solid water from -22.0 °C to 0 °C.
- The specific heat capacity of solid water is 2.09 J/g·°C.
- The mass of the solid water is 39.0 g.
- The change in temperature is 0 °C - (-22.0 °C) = 22.0 °C.
- Use the formula: energy = mass × specific heat capacity × change in temperature.
- Plug in the values: energy = 39.0 g × 2.09 J/g·°C × 22.0 °C.
2. Calculate the energy required to melt the solid water at 0 °C.
- The heat of fusion (energy required to melt one gram of solid to liquid at the melting point) for water is 334 J/g.
- The mass of the solid water is 39.0 g.
- Use the formula: energy = mass × heat of fusion.
- Plug in the values: energy = 39.0 g × 334 J/g.
3. Calculate the energy required to heat the liquid water from 0 °C to 100 °C.
- The specific heat capacity of liquid water is 4.18 J/g·°C.
- The mass of the liquid water is 39.0 g.
- The change in temperature is 100 °C - 0 °C = 100 °C.
- Use the formula: energy = mass × specific heat capacity × change in temperature.
- Plug in the values: energy = 39.0 g × 4.18 J/g·°C × 100 °C.
4. Calculate the energy required to vaporize the liquid water at 100 °C.
- The heat of vaporization (energy required to convert one gram of liquid to gas at the boiling point) for water is 2260 J/g.
- The mass of the liquid water is 39.0 g.
- Use the formula: energy = mass × heat of vaporization.
- Plug in the values: energy = 39.0 g × 2260 J/g.
5. Calculate the energy required to heat the water vapor from 100 °C to 163 °C.
- The specific heat capacity of water vapor is 2.03 J/g·°C.
- The mass of the water vapor is 39.0 g.
- The change in temperature is 163 °C - 100 °C = 63 °C.
- Use the formula: energy = mass × specific heat capacity × change in temperature.
- Plug in the values: energy = 39.0 g × 2.03 J/g·°C × 63 °C.
6. Sum up all the energies calculated in steps 1-5 to get the total energy required.
Remember to do the calculations accurately to get the correct answer.