Question

a sealed syringe contains oxygen gas (o₂) at a pressure of 115.0 kilopascals (kpa). the plunger of the syringe is depressed until the pressure and volume of the gas in the syringe are 190.0 kilopascals and 32 cubic centimeters, respectively. what was the initial volume of the o₂ gas in the syringe before the plunger was depressed? assume ideal gas behavior and a constant temperature. write your answer to the correct number of significant figures. round if necessary. cubic centimeters

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: Rearrange the formula to solve for $V_1$

$V_1=\frac{P_2V_2}{P_1}$.

Step3: Substitute the given values

Given $P_1 = 115.0\ kPa$, $P_2 = 190.0\ kPa$, and $V_2 = 32\ cm^3$. Then $V_1=\frac{190.0\ kPa\times32\ cm^3}{115.0\ kPa}$.

Step4: Calculate the value of $V_1$

$V_1=\frac{6080}{115.0}\ cm^3\approx52.87\ cm^3$. Rounding to two significant figures (since 32 has two significant figures), $V_1 = 53\ cm^3$.

Answer:

53