The combined gas law equation is expressed as:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure
V2 = final volume
T2 = final temperature
We are given:
P1 = 1 bar
V1 = 1.2 L
T1 = 300 K
P2 = 9 bars
T2 = 1200 K
Substituting the given values into the formula:
(1 bar * 1.2 L) / (300 K) = (9 bars * V2) / (1200 K)
Rearranging the equation to solve for V2:
(9 bars * V2) / (1200 K) = (1 bar * 1.2 L) / (300 K)
Cross-multiplying:
(9 bars * V2) * (300 K) = (1 bar * 1.2 L) * (1200 K)
(9 bars * V2) * (300 K) = (1.2 L) * (1200 K)
Canceling units:
2700 bars * V2 = 1440 L * K
Dividing both sides by 2700 bars:
V2 = (1440 L * K) / (2700 bars)
Simplifying:
V2 = 0.5333 L
Therefore, the new volume of the gas is approximately 0.5333 L.
A gas at 300 K and under 1 bar of pressure takes up 1.2 L of volume.
The gas is quickly compressed to 9 bars and the new temperature is measured to be 1200 K.
Use the combined gas law to calculate the new volume of the gas. Show your work!
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