Question

A 6.5 l sample of nitrogen at 25◦c and 1.5 atm is allowed to expand to 13.0 l. the temperature remains constant. what is the final pressure? 1. 0.75 atm 2. 3.0 atm 3. 0.063 atm 4. 0.38 atm 5. 0.12 atm

Answer 1

Since the temperature of the gas remains constant in the process, we can use Boyle's law, which states that for a gas transformation at constant temperature, the product between the gas pressure and its volume is constant:
$pV=k$
which can also be rewritten as
$p_1 V_1 = p_2 V_2$ (1)
where the labels 1 and 2 mark the initial and final conditions of the gas.

In our problem, $p_1 = 1.5 atm$, $V_1 =6.5 L$ and $V_2 =13.0 L$, so the final pressure of the gas can be found by re-arranging eq.(1):
$p_2 = p_1 \frac{V_1}{V_2}= (1.5 atm) \frac{6.5 L}{13.0 L}=0.75 atm$

Therefore the correct answer is
1. 0.75 atm