If a given mass of gas occupies a volume of 10 cc at 1 atmospheric pressure and temperature of 100°C (373.15 K). What will be its volume at 4 atmospheric pressure; the temperature being the same

The correct option is 2.5 cc.

Step-by-Step Explanation:

To find the new volume of the gas, we use the relationship between the pressure and volume of a gas when temperature and the quantity of the gas are kept constant. This is described by Boyle's Law.

1. Identify the given values:
Initial Pressure ($P_1$):
$P_1=1\text{atm}$
Initial Volume ($V_1$):
$V_1=10\text{cc}$
Final Pressure ($P_2$):
$P_2=4\text{atm}$
Temperature ($T$):
$T=100°\text{C}$ (constant)

2. State the formula (Boyle's Law):
Since the temperature remains constant, the volume of a given mass of gas is inversely proportional to its pressure:
$P_1{V}_1=P_2{V}_2$

3. Rearrange the formula to solve for the final volume ($V_2$):
$V_2=\frac{P_1{V}_1}{P_2}$

4. Substitute the values into the equation:
$V_2=\frac{1\text{atm}\times 10\text{cc}}{4\text{atm}}$

5. Calculate the final volume:
$V_2=2.5\text{cc}$

Thus, the final volume of the gas at 4 atmospheric pressure is 2.5 cc.