Question

if a certain gas occupies a volume of 14 l when the applied pressure is 7.0 atm, find the pressure when the gas occupies a volume of 35 l. express your answer to two significant figures and include the appropriate units.

Explanation:

Step1: Identify the gas - law formula

Boyle's law states $P_1V_1 = P_2V_2$, where $P_1$ and $V_1$ are the initial pressure and volume, and $P_2$ and $V_2$ are the final pressure and volume.

Step2: Substitute the given values

We are given $P_1 = 7.0$ atm, $V_1=14$ L, and $V_2 = 35$ L. Rearranging the formula for $P_2$ gives $P_2=\frac{P_1V_1}{V_2}$. Substituting the values: $P_2=\frac{7.0\ atm\times14\ L}{35\ L}$.

Step3: Calculate the result

$P_2=\frac{98}{35}$ atm $ = 2.8$ atm. But we need to consider significant - figures. Since 7.0 has two significant figures, 14 has two significant figures, and 35 has two significant figures, our final answer should also have two significant figures. So $P_2 = 2.8$ atm.

Answer:

$2.8$ atm