Answer :

To find the pressure of an ideal gas, we use the ideal gas law, which is expressed as:

[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 ideal gas constant,
- [tex]\( T \)[/tex] is the temperature in Kelvin.

Let's go through the solution step-by-step:

1. Convert the Temperature to Kelvin:

The temperature given is in degrees Celsius. To convert it to Kelvin, use the formula:

[tex]\[ T(K) = T(^\circ C) + 273.15 \][/tex]

For this problem:

[tex]\[ T = 75 + 273.15 = 348.15 \, \text{K} \][/tex]

2. Identify the Given Values:

- Moles of gas, [tex]\( n = 78.5 \, \text{mol} \)[/tex]
- Volume of the gas, [tex]\( V = 38.5 \, \text{L} \)[/tex]
- Ideal gas constant, [tex]\( R = 0.0821 \, \text{L·atm/(K·mol)} \)[/tex]

3. Rearrange the Ideal Gas Law to Solve for Pressure (P):

The formula can be rearranged to solve for pressure:

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

4. Calculate the Pressure:

Substitute the known values into the equation:

[tex]\[ P = \frac{78.5 \times 0.0821 \times 348.15}{38.5} \][/tex]

5. Result:

The calculated pressure is approximately:

[tex]\[ P \approx 58.28 \, \text{atm} \][/tex]

Therefore, the pressure of the gas is [tex]\( 58.28 \, \text{atm} \)[/tex].

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