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.

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.

$\frac{P_{1}V_{1}}{T_{1}} = \frac{P_{2}V_{2}}{T_{2}}$

Substitute the values into above formula as follows.

$\frac{P_{1}V_{1}}{T_{1}} = \frac{P_{2}V_{2}}{T_{2}}\\\frac{2.7 atm \times 3.1 L}{300 K} = \frac{P_{2} \times 9.4 L}{610 K}\\P_{2} = \frac{5105.7}{2820} atm\\= 1.81 atm$

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

$P_{2}V_{2} = n_{2}RT_{2}\\1.81 atm \times 9.4 L = n_{2} \times 0.0821 L atm/mol K \times 610 K\\n_{2} = \frac{17.014}{50.081} mol\\= 0.34 mol$

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