Question

a sealed syringe contains neon gas (ne) at a pressure of 5.51 atmospheres (atm). the plunger of the syringe is pulled back until the pressure and volume of the gas in the syringe are 4.45 atmospheres and 0.046 liters, respectively. what was the initial volume of the ne gas in the syringe before the plunger was pulled back? 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

$P_1V_1 = P_2V_2$

Step2: Define the variables

$P_1 = 5.51$ atm, $P_2=4.45$ atm, $V_2 = 0.046$ L, $V_1$ is the unknown initial - volume.

Step3: Rearrange the formula to solve for $V_1$

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

Step4: Substitute the values

$V_1=\frac{4.45\text{ atm}\times0.046\text{ L}}{5.51\text{ atm}}$
$V_1=\frac{0.2047}{5.51}\text{ L}$
$V_1 = 0.0371506352$ L

Step5: Round to the correct number of significant figures

Since 4.45 and 0.046 have 3 and 2 significant figures respectively, we round to 2 significant figures. So $V_1 = 0.037$ L

Answer:

0.037 liters