Question

a sample of carbon dioxide gas (co₂) at a pressure of 574.1 kilopascals (kpa) is transferred from a tank to an empty cylinder with a volume of 3.5 × 10⁻³ cubic meters. after transfer, the pressure of the gas in the cylinder is 1,946.5 kilopascals. what was the initial volume of the co₂ gas inside the tank? assume ideal gas behavior and a constant temperature. write your answer to the correct number of significant figures. round if necessary. cubic meters save answer

Explanation:

Step1: Recall Boyle's Law

Boyle's Law states that for a given mass of an ideal gas at constant temperature, the product of pressure and volume is constant, i.e., $P_1V_1 = P_2V_2$. Here, $P_1 = 574.1\space kPa$, $V_2 = 3.5\times 10^{-3}\space m^3$, and $P_2 = 1946.5\space kPa$. We need to find $V_1$.

Step2: Rearrange the formula to solve for $V_1$

From $P_1V_1 = P_2V_2$, we can rearrange it to $V_1=\frac{P_2V_2}{P_1}$.

Step3: Substitute the given values into the formula

Substitute $P_1 = 574.1\space kPa$, $V_2 = 3.5\times 10^{-3}\space m^3$, and $P_2 = 1946.5\space kPa$ into the formula:

$$
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(We consider significant figures: $3.5$ has two significant figures, so the final answer should have two significant figures.)

Answer:

$1.2\times 10^{-2}$