Question

If you have 1.14 mol of CO2 at a pressure of 3.4 atm and a temperature of 100oC, what will the volume be?
Responses

118.7 Liters
118.7 Liters

19.6 Liters
19.6 Liters

10.27 Liters
10.27 Liters

0.0973 Liters

Answer 1

To find the volume of carbon dioxide (CO₂) given the number of moles, pressure, and temperature, we can use the Ideal Gas Law equation:

\[
PV = nRT
\]

Where:
- \( P \) = pressure in atm
- \( V \) = volume in liters
- \( n \) = number of moles
- \( R \) = ideal gas constant (\( 0.0821 \, \text{L} \cdot \text{atm} / \text{K} \cdot \text{mol} \))
- \( T \) = temperature in Kelvin

### Step 1: Convert temperature to Kelvin

The temperature must be in Kelvin for the Ideal Gas Law:

\[
T(K) = T(°C) + 273.15 = 100°C + 273.15 = 373.15 \, K
\]

### Step 2: Plug in values into the Ideal Gas Law

We are given:
- \( n = 1.14 \, \text{mol} \)
- \( P = 3.4 \, \text{atm} \)
- \( R = 0.0821 \, \text{L} \cdot \text{atm} / \text{K} \cdot \text{mol} \)
- \( T = 373.15 \, K \)

Now we can rearrange the equation to solve for \( V \):

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

Substituting in the values:

\[
V = \frac{(1.14 \, \text{mol}) \times (0.0821 \, \text{L} \cdot \text{atm} / \text{K} \cdot \text{mol}) \times (373.15 \, K)}{3.4 \, \text{atm}}
\]

### Step 3: Calculate

Now let's compute the value step by step:

- Calculate the numerator:

\[
1.14 \times 0.0821 \times 373.15 \approx 35.052
\]

- Calculate the volume:

\[
V = \frac{35.052}{3.4} \approx 10.27 \, \text{L}
\]

Therefore, the volume of CO₂ under the given conditions is approximately **10.27 Liters**.

### Conclusion

The correct answer is **10.27 Liters**.