A sample of gas has an initial volume of 2.4 L at a pressure of 855 mm Hg and a temperature of 298K. If the gas is heated to a temperature of 387 K and expanded to a volume of 4.1 L, what is its final pressure in mm of mercury?
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To find the final pressure of the gas, we can use the combined gas law equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure (what we're trying to find)
V2 = final volume
T2 = final temperature
Let's plug in the given values into the equation:
(855 mm Hg * 2.4 L) / 298 K = (P2 * 4.1 L) / 387 K
Now let's solve for P2, the final pressure:
(855 mm Hg * 2.4 L * 387 K) / (298 K * 4.1 L) = P2
P2 ≈ 808 mm Hg
Therefore, the final pressure of the gas is approximately 808 mm Hg.
To solve this problem, we can use the combined gas law, which states:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure (what we're trying to find)
V2 = final volume
T2 = final temperature
Given:
P1 = 855 mm Hg
V1 = 2.4 L
T1 = 298 K
V2 = 4.1 L
T2 = 387 K
Substituting these values into the equation, we have:
(855 mm Hg * 2.4 L) / (298 K) = (P2 * 4.1 L) / (387 K)
To find the final pressure (P2), we need to isolate it. Let's rearrange the equation:
P2 = (855 mm Hg * 2.4 L * 387 K) / (4.1 L * 298 K)
Now, let's calculate the final pressure using the equation:
P2 = (855 mm Hg * 2.4 L * 387 K) / (4.1 L * 298 K)
= 1664.8 mm Hg
Therefore, the final pressure of the gas is approximately 1664.8 mm Hg.