Question

A cylinder contains 3.1 L of oxygen at 300 K and 2.7 atm. The gas is heated, causing a piston in the cylinder to move outward. The heating causes the temperature to rise to 610 K and the volume of the cylinder to increase to 9.4 L.

How many moles of gas are in the cylinder?
Express your answer using two significant figures.

Answer 1

Answer: The moles of gas present in the cylinder is 0.34 moles.

Step-by-step explanation:

Given:
`P_(1)` = 2.7 atm,
`V_(1)` = 3.1 L,
`T_(1)` = 300 K

`P_(2)` = ?,
`V_(2)` = 9.4 L,
`T_(2)` = 610 K

Formula used to calculate the final temperature is as follows.

`(P_(1)V_(1))/(T_(1)) = (P_(2)V_(2))/(T_(2))`

Substitute the values into above formula as follows.

`(P_(1)V_(1))/(T_(1)) = (P_(2)V_(2))/(T_(2))\\(2.7 atm * 3.1 L)/(300 K) = (P_(2) * 9.4 L)/(610 K)\\P_(2) = (5105.7)/(2820) atm\\= 1.81 atm`

Now, moles present upon heating the cylinder are as follows.

`P_(2)V_(2) = n_(2)RT_(2)\\1.81 atm * 9.4 L = n_(2) * 0.0821 L atm/mol K * 610 K\\n_(2) = (17.014)/(50.081) mol\\= 0.34 mol`

Thus, we can conclude that moles of gas present in the cylinder is 0.34 moles.