The temperature of a 89.869 L sample of SeF6 is changed, causing a change in pressure from 84.42 PSI to 6.18 atm. If its new temperature is 1020.1 K and its new volume is 21.962 L, what was its original temperature in kelvins?
Question
The temperature of a 89.869 L sample of SeF6 is changed, causing a change in pressure from 84.42 PSI to 6.18 atm. If its new temperature is 1020.1 K and its new volume is 21.962 L, what was its original temperature in kelvins?
Solution
To solve this problem, we can use the combined gas law which states that the ratio of the product of pressure and volume to temperature is constant for a given amount of gas. The formula is:
P1V1/T1 = P2V2/T2
Where: P1 = initial pressure V1 = initial volume T1 = initial temperature (which we are trying to find) P2 = final pressure V2 = final volume T2 = final temperature
First, we need to convert the pressures to the same units. We'll convert PSI to atm because the final pressure is given in atm. 1 atm = 14.696 PSI. So, the initial pressure in atm is 84.42 PSI / 14.696 = 5.74 atm.
Now we can plug the values into the formula and solve for T1:
5.74 atm * 89.869 L / T1 = 6.18 atm * 21.962 L / 1020.1 K
Rearranging the formula to solve for T1 gives:
T1 = 5.74 atm * 89.869 L * 1020.1 K / (6.18 atm * 21.962 L)
Calculating this gives:
T1 = 448.6 K
So, the original temperature of the gas was approximately 448.6 kelvins.
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