Question

a balloon filled with hydrogen gas (h₂) has an internal pressure of 1.268 bar and a volume of 5.000×10⁻³ cubic meters when squeezed. releasing the balloon causes the pressure to decrease to 1.100 bar. what is the final volume of the h₂ gas in the balloon? assume ideal gas behavior and a constant temperature. write your answer to the correct number of significant figures. round if necessary.

Explanation:

Step1: Identify Boyle's Law formula

Boyle's Law is $P_1V_1 = P_2V_2$, where $P_1$ and $V_1$ are initial - pressure and volume, and $P_2$ and $V_2$ are final - pressure and volume.

Step2: Assign given values

$P_1=1.268$ bar, $V_1 = 5.000\times10^{-3}$ m³, $P_2 = 1.100$ bar. We need to find $V_2$.

Step3: Rearrange the formula to solve for $V_2$

$V_2=\frac{P_1V_1}{P_2}$.

Step4: Substitute the values

$V_2=\frac{1.268\ bar\times5.000\times 10^{-3}\ m^{3}}{1.100\ bar}$.
$V_2=\frac{1.268\times5.000\times 10^{-3}}{1.100}\ m^{3}$.
$V_2=\frac{6.34\times 10^{-3}}{1.100}\ m^{3}\approx5.764\times 10^{-3}\ m^{3}$.

Answer:

$5.76\times 10^{-3}$ m³ (rounded to three significant figures)