Question

part b
a 20.0 l gas cylinder is filled with 8.00 moles of gas. the tank is stored at 21 °c. what is the pressure in the tank?
express your answer to three significant figures and include the appropriate units.
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p_tank =
part c
a 240. l kiln is used for vitrifying ceramics. it is currently operating at 875 °c, and the pressure is 0.9000 atm. how many moles of air molecules are within the confines of the kiln?
express your answer to three significant figures and include the appropriate units.

Explanation:

Step1: Identify the gas law

We use the ideal gas law, \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is moles, \( R \) is the gas constant, and \( T \) is temperature in Kelvin.

Step2: Convert temperature to Kelvin

\( T = 21^\circ\text{C} + 273.15 = 294.15\,\text{K} \)

Step3: Rearrange the ideal gas law to solve for \( P \)

\( P=\frac{nRT}{V} \)

Step4: Substitute the values

\( n = 8.00\,\text{mol} \), \( R = 0.0821\,\frac{\text{L}\cdot\text{atm}}{\text{mol}\cdot\text{K}} \), \( T = 294.15\,\text{K} \), \( V = 20.0\,\text{L} \)
\( P=\frac{8.00\,\text{mol} \times 0.0821\,\frac{\text{L}\cdot\text{atm}}{\text{mol}\cdot\text{K}} \times 294.15\,\text{K}}{20.0\,\text{L}} \)

Step5: Calculate the pressure

First, calculate the numerator: \( 8.00 \times 0.0821 \times 294.15 \approx 8.00 \times 24.15 \approx 193.2 \)
Then divide by volume: \( \frac{193.2}{20.0} = 9.66\,\text{atm} \)

Answer:

\( 9.66\,\text{atm} \)