Questions: If the cylinder, shown below is 5.5 L big, has a pressure of 2.47 atm and the temperature in the room is 39°C, how many moles of gas are in the cylinder? (answer to 1/100 place X.XX)

Solution Steps

To use the ideal gas law, we need the temperature in Kelvin. The conversion from Celsius to Kelvin is given by:

\[ T(K) = T(^{\circ}C) + 273.15 \]

For this problem:

\[ T = 39 + 273.15 = 312.15 \, \text{K} \]

The ideal gas law is given by:

\[ PV = nRT \]

where:

• \( P \) is the pressure in atm,
• \( V \) is the volume in liters,
• \( n \) is the number of moles,
• \( R \) is the ideal gas constant, \( R = 0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1} \),
• \( T \) is the temperature in Kelvin.

We need to solve for \( n \):

\[ n = \frac{PV}{RT} \]

Substitute the given values into the equation:

\[ n = \frac{(2.47 \, \text{atm})(5.5 \, \text{L})}{(0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1})(312.15 \, \text{K})} \]

Perform the calculation:

\[ n = \frac{13.585}{25.624215} \approx 0.5301 \]

Final Answer