To solve this problem, we can use Charles’s Law, which states that the volume of a gas is directly proportional to its temperature when pressure and amount of gas are kept constant. Mathematically, it can be expressed as:
V1 / T1 = V2 / T2
Where: V1 = initial volume of the gas T1 = initial temperature of the gas V2 = final volume of the gas (to be determined) T2 = final temperature of the gas
Given: V1 = 546 cm^3 T1 = 0°C (273 K) [Note: Temperature must be in Kelvin scale for this equation.]
We need to find V2 when T2 = 2°C.
Let’s substitute the values into the equation and solve for V2:
V1 / T1 = V2 / T2
546 cm^3 / 273 K = V2 / (2°C + 273 K) 2 cm^3/K = V2 / 275 K
Cross-multiplying: 2 cm^3/K * 275 K = V2 V2 = 550 cm^3
Therefore, the volume of the gas at 2°C is 550 cm^3.