At N.T.P the volume of a gas is found to be 150mL. What will be the volume of this gas at 600mm Hg and `237^o`C?

Options

A. 330.49
B. 479.78
C. 297.74
D. 104.23

Explanation

To solve the problem, we will use the ideal gas law, which states that the relationship between pressure (P), volume (V), and temperature (T) of a gas can be expressed as:

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

Where:
- \(P_1\) = Initial pressure
- \(V_1\) = Initial volume
- \(T_1\) = Initial temperature (in Kelvin)
- \(P_2\) = Final pressure
- \(V_2\) = Final volume (what we want to find)
- \(T_2\) = Final temperature (in Kelvin)

### Step 1: Identify the known values
- Initial volume, \(V_1 = 150 \, \text{mL}\)
- Initial pressure, \(P_1 = 1 \, \text{atm}\) (at NTP)
- Initial temperature, \(T_1 = 293 \, \text{K}\) (NTP)
- Final pressure, \(P_2 = 600 \, \text{mm Hg}\)
- Final temperature, \(T_2 = 237 \, \text{°C}\)

### Step 2: Convert the final pressure to atm
To convert mm Hg to atm, we use the conversion factor:
\[ 1 \, \text{atm} = 760 \, \text{mm Hg} \]
Thus,
\[ P_2 = \frac{600 \, \text{mm Hg}}{760 \, \text{mm Hg/atm}} = 0.7895 \, \text{atm} \]

### Step 3: Convert the final temperature to Kelvin
To convert Celsius to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273.15 \]
Thus,
\[ T_2 = 237 + 273.15 = 510.15 \, \text{K} \]

### Step 4: Substitute the values into the ideal gas law equation
Now we can substitute the known values into the equation:
\[ \frac{1 \, \text{atm} \times 150 \, \text{mL}}{293 \, \text{K}} = \frac{0.7895 \, \text{atm} \times V_2}{510.15 \, \text{K}} \]

### Step 5: Solve for \(V_2\)
Rearranging the equation to solve for \(V_2\):
\[ V_2 = \frac{1 \, \text{atm} \times 150 \, \text{mL} \times 510.15 \, \text{K}}{293 \, \text{K} \times 0.7895 \, \text{atm}} \]

Calculating:
\[ V_2 = \frac{150 \times 510.15}{293 \times 0.7895} \]

Calculating the numerator:
\[ 150 \times 510.15 = 76522.5 \]

Calculating the denominator:
\[ 293 \times 0.7895 = 231.7935 \]

Now, dividing:
\[ V_2 = \frac{76522.5}{231.7935} \approx 330.49 \, \text{mL} \]

### Final Answer
The volume of the gas at 600 mm Hg and 237 °C is approximately **330.49 mL**.

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