High School

If 46.5 mol of an ideal gas occupies 64.5 L at 345 K, what is the pressure of the gas?

Pressure: _____ atm

Answer :

To find the pressure of an ideal gas given the number of moles, volume, and temperature, we can use the Ideal Gas Law equation, which is:

[tex]\[ PV = nRT \][/tex]

Where:
- [tex]\( P \)[/tex] is the pressure of the gas,
- [tex]\( V \)[/tex] is the volume of the gas,
- [tex]\( n \)[/tex] is the number of moles of the gas,
- [tex]\( R \)[/tex] is the universal gas constant, and
- [tex]\( T \)[/tex] is the temperature in Kelvin.

Now, let's solve for the pressure [tex]\( P \)[/tex]:

1. Identify the given values:
- Number of moles of the gas, [tex]\( n = 46.5 \)[/tex] mol.
- Volume of the gas, [tex]\( V = 64.5 \)[/tex] L.
- Temperature, [tex]\( T = 345 \)[/tex] K.
- The universal gas constant, [tex]\( R = 0.0821 \, \text{L} \cdot \text{atm}/\text{K} \cdot \text{mol} \)[/tex].

2. Substitute the values into the equation:

[tex]\[
P = \frac{nRT}{V}
\][/tex]

3. Calculate the pressure [tex]\( P \)[/tex]:

[tex]\[
P = \frac{(46.5 \, \text{mol}) \times (0.0821 \, \text{L} \cdot \text{atm}/\text{K} \cdot \text{mol}) \times (345 \, \text{K})}{64.5 \, \text{L}}
\][/tex]

[tex]\[
P \approx 20.42 \, \text{atm}
\][/tex]

Therefore, the pressure of the gas is approximately 20.42 atm.