A quantity of N2 occupies a volume of 1.5 L at 300 K and 1.2 atm . The gas expands to a volume of 3.2 L as the result of a change in both temperature and pressure.
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To find the new temperature and pressure after the gas expands from 1.5 L to 3.2 L, we need to apply the combined gas law. The combined gas law relates the initial and final conditions of a gas sample assuming the amount of gas remains constant.
The combined gas law equation is as follows:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 = initial pressure (1.2 atm)
V1 = initial volume (1.5 L)
T1 = initial temperature (300 K)
P2 = final pressure (unknown)
V2 = final volume (3.2 L)
T2 = final temperature (unknown)
We can rearrange the equation to solve for the final pressure (P2) and final temperature (T2):
P2 = (P1 * V1 * T2) / (V2 * T1)
Substituting the given values into the equation:
P2 = (1.2 atm * 1.5 L * T2) / (3.2 L * 300 K)
Simplifying the equation:
P2 = (0.9 * T2) / 0.8
Now, let's solve for the final pressure (P2) at a given final temperature (T2).