an old 0.500 l lecture bottle of ch₄ was found in a lab and needed for a reaction. a pressure regulator…

an old 0.500 l lecture bottle of ch₄ was found in a lab and needed for a reaction. a pressure regulator indicated a pressure of 46.5 psi, and the lab was at room temperature (25 °c). what mass of gaseous ch₄ was left in the lecture bottle?

an old 0.500 l lecture bottle of ch₄ was found in a lab and needed for a reaction. a pressure regulator indicated a pressure of 46.5 psi, and the lab was at room temperature (25 °c). what mass of gaseous ch₄ was left in the lecture bottle?

Answer

Answer:

0.137 g

Explanation:

Step1: Convert units

First, convert pressure from psi to atm. 1 psi = 0.068046 atm, so $P = 46.5\times0.068046\ atm\approx 3.164\ atm$. Convert temperature from $^{\circ}C$ to K, $T=(25 + 273.15)\ K=298.15\ K$, and $V = 0.500\ L$.

Step2: Use ideal - gas law

The ideal - gas law is $PV=nRT$, where $R = 0.0821\ L\cdot atm/(mol\cdot K)$. Solve for $n$ (number of moles): $n=\frac{PV}{RT}$. Substitute the values: $n=\frac{3.164\ atm\times0.500\ L}{0.0821\ L\cdot atm/(mol\cdot K)\times298.15\ K}\approx0.00856\ mol$.

Step3: Calculate mass

The molar mass of $CH_4$ is $M=(12.01 + 4\times1.008)\ g/mol = 16.042\ g/mol$. Use the formula $m = nM$. So $m=0.00856\ mol\times16.042\ g/mol\approx0.137\ g$.