At `27^(@)`C and 500 mm Hg pressure a gas occupies 400mL volume.
What will be its pressure at a height where temp is `7^(@)`C and
volume is 550 mL :-

Options

A. 340mm
B. 240mm
C. 440mm
D. 540mm

Explanation

To solve the problem, we will use the combined gas law, which relates pressure, volume, and temperature of a gas. The formula is:

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

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

### Step 1: Convert temperatures from Celsius to Kelvin
- For \(T_1\) (27°C):
\[ T_1 = 27 + 273 = 300 \text{ K} \]
- For \(T_2\) (7°C):
\[ T_2 = 7 + 273 = 280 \text{ K} \]

### Step 2: Identify the given values
- \(P_1 = 500 \text{ mm Hg}\)
- \(V_1 = 400 \text{ mL}\)
- \(T_1 = 300 \text{ K}\)
- \(V_2 = 550 \text{ mL}\)
- \(T_2 = 280 \text{ K}\)

### Step 3: Substitute the known values into the combined gas law equation
\[ \frac{500 \times 400}{300} = \frac{P_2 \times 550}{280} \]

### Step 4: Rearrange the equation to solve for \(P_2\)
\[ P_2 = \frac{500 \times 400 \times 280}{300 \times 550} \]

### Step 5: Calculate \(P_2\)
\[ P_2 = \frac{500 \times 400 \times 280}{300 \times 550} \]
Calculating the numerator:
\[ 500 \times 400 \times 280 = 56000000 \]
Calculating the denominator:
\[ 300 \times 550 = 165000 \]
Now divide:
\[ P_2 = \frac{56000000}{165000} \approx 339.39 \text{ mm Hg} \]

### Step 6: Round the answer
The final pressure \(P_2\) is approximately:
\[ P_2 \approx 340 \text{ mm Hg} \]

### Final Answer
The pressure at a height where the temperature is 7°C and the volume is 550 mL is approximately **340 mm Hg**.

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