A chemistry reactor with a constant volume of 1.0 L is sealed with an internal pressure of 350.0 psi at 27.0 °C. When the reactor is heated to 120 °C, what will the pressure become... A chemistry reactor with a constant volume of 1.0 L is sealed with an internal pressure of 350.0 psi at 27.0 °C. When the reactor is heated to 120 °C, what will the pressure become?
Understand the Problem
The question is asking us to calculate the change in pressure of a sealed chemistry reactor when the temperature is increased from 27.0 °C to 120 °C, given that the volume remains constant. We will use the ideal gas law or the principles of direct proportionality between pressure and temperature (in Kelvin) to solve this problem.
Answer
$$ P_2 = P_1 \cdot \frac{393.15}{300.15} $$
Answer for screen readers
The final pressure, if starting from an initial pressure ( P_1 ), is given by:
$$ P_2 = P_1 \cdot \frac{393.15}{300.15} $$
Steps to Solve
- Convert Temperatures to Kelvin
To use the ideal gas law, we must convert the given temperatures from Celsius to Kelvin. The formula to convert Celsius to Kelvin is:
$$ K = C + 273.15 $$
So, for 27.0 °C:
$$ T_1 = 27.0 + 273.15 = 300.15 , K $$
And for 120.0 °C:
$$ T_2 = 120.0 + 273.15 = 393.15 , K $$
- Use the Pressure-Temperature Relationship
Since the volume is constant, we can use the relationship between pressure and temperature directly. According to Gay-Lussac's Law, the ratio of the pressure to temperature remains constant:
$$ \frac{P_1}{T_1} = \frac{P_2}{T_2} $$
We can rearrange this to find the new pressure ( P_2 ):
$$ P_2 = P_1 \cdot \frac{T_2}{T_1} $$
- Calculate the New Pressure
If we assume an initial pressure ( P_1 ) (you can substitute in any initial pressure value as long as it remains consistent), we substitute the values of ( T_1 ) and ( T_2 ):
$$ P_2 = P_1 \cdot \frac{393.15}{300.15} $$
We can simplify this expression to find the change in pressure.
The final pressure, if starting from an initial pressure ( P_1 ), is given by:
$$ P_2 = P_1 \cdot \frac{393.15}{300.15} $$
More Information
This result shows how pressure increases with temperature in a constant volume setup. This is an application of the ideal gas law, emphasizing the direct relationship between pressure and temperature.
Tips
- Failing to convert Celsius to Kelvin before performing calculations.
- Forgetting that pressure increases proportionally with temperature when volume is constant.
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