Question

A cylinder contains a gas: volume of 2.7 L, pressure of 850 Torr, 25 degrees C. What is the temperature if the gas is compressed to 1.9L, pressure of 900 Torr

Answer 1

To find the new temperature of the gas after it has been compressed, we can use the combined gas law, which is given by the equation:

\[
\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}
\]

Where:
- \( P_1 \) = initial pressure
- \( V_1 \) = initial volume
- \( T_1 \) = initial temperature in Kelvin
- \( P_2 \) = final pressure
- \( V_2 \) = final volume
- \( T_2 \) = final temperature in Kelvin

### Step 1: Convert the initial temperature to Kelvin
The initial temperature (\( T_1 \)) is given as 25 degrees Celsius. To convert this to Kelvin:

\[
T_1 = 25 + 273.15 = 298.15 \, K
\]

### Step 2: Identify the initial and final states
Given data:
- \( P_1 = 850 \, \text{Torr} \)
- \( V_1 = 2.7 \, \text{L} \)
- \( T_1 = 298.15 \, K \)
- \( P_2 = 900 \, \text{Torr} \)
- \( V_2 = 1.9 \, \text{L} \)

### Step 3: Rearranging the combined gas law to solve for \( T_2 \)
We rearrange the combined gas law equation to solve for \( T_2 \):

\[
T_2 = \frac{P_2 V_2 T_1}{P_1 V_1}
\]

### Step 4: Plugging in the values
Now substitute in the known values:

\[
T_2 = \frac{(900 \, \text{Torr}) (1.9 \, \text{L}) (298.15 \, K)}{(850 \, \text{Torr}) (2.7 \, \text{L})}
\]

### Step 5: Calculate \( T_2 \)
Calculating the numerator and the denominator:

**Numerator:**
\[
900 \times 1.9 \times 298.15 = 537,391.5
\]

**Denominator:**
\[
850 \times 2.7 = 2,295
\]

Now calculating \( T_2 \):

\[
T_2 = \frac{537,391.5}{2,295} \approx 234.37 \, K
\]

### Conclusion
The final temperature \( T_2 \) of the gas after compression is approximately **234.37 K**.