determine the quantity of heat needed to convert 17.0g of solid mercury at -50.0C to mercury vapor at 25C . Specific heats: , 24.3C , , 28.0C . Melting point of hg, -38.87C . Heat of fusion, 2.33 .
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To determine the quantity of heat needed to convert a solid substance to vapor, we need to consider the heat required for three different processes: raising the temperature of the solid to its melting point, melting the solid at its melting point, and raising the temperature of the liquid to the desired final temperature.
1. Raising the temperature of the solid to its melting point:
First, we calculate the heat required to raise the temperature of the solid mercury to its melting point. We use the formula: Q = m * C * ΔT, where Q is the heat required, m is the mass, C is the specific heat, and ΔT is the change in temperature.
Given:
- Mass (m) = 17.0g
- Specific heat (C) = 24.3 J/g°C
- Change in temperature (ΔT) = (Melting point of Hg) - (-50.0°C) = -38.87°C - (-50.0°C)
Calculating the heat required for this step:
Q1 = 17.0g * 24.3 J/g°C * (-38.87°C - (-50.0°C))
2. Melting the solid at its melting point:
The heat of fusion (ΔHfus) is the amount of heat required to change the solid into a liquid at its melting point. Given that ΔHfus for mercury is 2.33 J/g, we can calculate the heat required using the formula: Q = m * ΔHfus.
Given:
- Mass (m) = 17.0g
- ΔHfus = 2.33 J/g
Calculating the heat required for this step:
Q2 = 17.0g * 2.33 J/g
3. Raising the temperature of the liquid to the desired final temperature:
Similar to step 1, we calculate the heat required to raise the temperature of the liquid mercury from its melting point to the desired final temperature. We use the formula: Q = m * C * ΔT.
Given:
- Mass (m) = 17.0g
- Specific heat (C) = 28.0 J/g°C
- Change in temperature (ΔT) = 25.0°C - (Melting point of Hg)
Calculating the heat required for this step:
Q3 = 17.0g * 28.0 J/g°C * (25.0°C - (Melting point of Hg))
Now, we can calculate the total quantity of heat required:
Total Q = Q1 + Q2 + Q3
You can substitute the given values into the equations to obtain the final answer.