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!
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.
The combined gas law relates the initial and final conditions of a gas system. It can be written 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
Given values:
P1 = 1 bar
V1 = 1.2 L
T1 = 300 K
P2 = 9 bar
T2 = 1200 K
Now we can rearrange the equation to solve for V2:
V2 = (P1 * V1 * T2) / (P2 * T1)
Plugging in the values:
V2 = (1 bar * 1.2 L * 1200 K) / (9 bar * 300 K)
Simplifying:
V2 = (1.2 * 1200) / (9 * 300)
V2 = 1440 / 2700
V2 = 0.533 L
Therefore, the new volume of the gas is approximately 0.533 L.
To solve this problem, we can use the combined gas law, which relates the pressure, volume, and temperature of a gas sample. The formula for the combined gas law is:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 is the initial pressure (1 bar)
V1 is the initial volume (1.2 L)
T1 is the initial temperature (300 K)
P2 is the final pressure (9 bars)
V2 is the final volume (we need to calculate this)
T2 is the final temperature (1200 K)
Now, let's substitute the given values into the formula and solve for V2:
(1 bar * 1.2 L) / 300 K = (9 bars * V2) / 1200 K
Cross multiplying:
1.2 * 1200 = 9 * V2
1440 = 9 * V2
Dividing both sides by 9:
V2 = 160 L
Therefore, the new volume of the gas is 160 L.