In a gas sound travels at a speed of `315 ms^(-1)` at NTP, If `R=8.3J mol^(-1) K^(-1)` identify the gas.

Answer

To identify the gas based on the speed of sound in it, we can use the formula for the speed of sound in a gas, which is given by:

\[ v = \sqrt{\frac{\gamma RT}{M}} \]

Where:
- \( v \) is the speed of sound in the gas (in m/s)
- \( \gamma \) is the adiabatic index (ratio of specific heats, \( C_p/C_v \))
- \( R \) is the universal gas constant (in J/(mol·K))
- \( T \) is the absolute temperature (in K)
- \( M \) is the molar mass of the gas (in kg/mol)

### Step-by-step Solution:

1. **Identify the Known Values:**
- Speed of sound, \( v = 315 \, \text{m/s} \)
- Gas constant, \( R = 8.3 \, \text{J/(mol·K)} \)
- Temperature at NTP (Normal Temperature and Pressure) is \( 0^\circ C \), which converts to Kelvin as:
\[ T = 273 \, \text{K} \]
- For diatomic gases like oxygen, \( \gamma \) is typically \( 1.4 \).

2. **Rearranging the Formula:**
We need to find the molar mass \( M \). Rearranging the speed of sound formula gives us:
\[ M = \frac{\gamma RT}{v^2} \]

3. **Substituting the Known Values:**
Now substitute the known values into the rearranged formula:
\[ M = \frac{1.4 \times 8.3 \times 273}{(315)^2} \]

4. **Calculating the Values:**
- First, calculate the numerator:
\[ 1.4 \times 8.3 \times 273 = 3205.14 \]
- Then calculate the denominator:
\[ (315)^2 = 99225 \]
- Now, substitute these values into the equation for \( M \):
\[ M = \frac{3205.14}{99225} \approx 0.0323 \, \text{kg/mol} \]

5. **Converting to grams:**
Since molar mass is often expressed in grams per mole, convert kilograms to grams:
\[ M \approx 32.3 \, \text{g/mol} \]

6. **Identifying the Gas:**
The molar mass of approximately \( 32 \, \text{g/mol} \) corresponds to oxygen (O₂), which has a molar mass of about \( 32 \, \text{g/mol} \).

### Final Answer:
The gas is **Oxygen (O₂)**.