High School

If 20.5 mol of an ideal gas occupies 46.5 L at 389 K, what is the pressure of the gas?

Pressure: ___ atm

Answer :

To find the pressure of the gas, we can use the Ideal Gas Law, which is expressed by the equation:

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

Where:
- [tex]\( P \)[/tex] is the pressure in atmospheres (atm).
- [tex]\( V \)[/tex] is the volume in liters (L).
- [tex]\( n \)[/tex] is the amount of substance in moles (mol).
- [tex]\( R \)[/tex] is the ideal gas constant, which is [tex]\( 0.0821 \, \text{atm} \cdot \text{L} / (\text{mol} \cdot \text{K}) \)[/tex].
- [tex]\( T \)[/tex] is the temperature in Kelvin (K).

Given:
- The amount of gas, [tex]\( n = 20.5 \, \text{mol} \)[/tex]
- The volume, [tex]\( V = 46.5 \, \text{L} \)[/tex]
- The temperature, [tex]\( T = 389 \, \text{K} \)[/tex]

We need to find the pressure [tex]\( P \)[/tex].

Step-by-step solution:

1. Start with the Ideal Gas Law: [tex]\[ PV = nRT \][/tex]

2. Rearrange the equation to solve for pressure [tex]\( P \)[/tex]:

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

3. Substitute the known values into the equation:

[tex]\[ P = \frac{(20.5 \, \text{mol}) \times (0.0821 \, \text{atm} \cdot \text{L} / (\text{mol} \cdot \text{K})) \times (389 \, \text{K})}{46.5 \, \text{L}} \][/tex]

4. Calculate the pressure:

[tex]\[ P \approx 14.08 \, \text{atm} \][/tex]

Therefore, the pressure of the gas is approximately 14.08 atm.