Final answer:
The temperature at which the volume of a gas increases from 1.78 L to 2.55 L can be calculated using Charles's Law. After converting the given temperature to Kelvin, the formula V1/T1 = V2/T2 is used, resulting in a new temperature of 172.23°C.
Step-by-step explanation:
To find the temperature at which the volume of a gas increases from 1.78 L to 2.55 L, we can use Charles's Law, which states that, for a given mass of an ideal gas at constant pressure, the volume is directly proportional to its absolute temperature. The formula to express Charles's Law is V1/T1 = V2/T2, where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature respectively.
First, we must convert the initial temperature from Celsius to Kelvin: T1(K) = 37.5°C + 273.15 = 310.65 K. Simply plug in the known values into the formula:
- V1 = 1.78 L
- T1 = 310.65 K
- V2 = 2.55 L
Using the formula, we solve for T2: T2 = (V2 × T1) / V1T2 = (2.55 L × 310.65 K) / 1.78 L
Calculating this gives us: T2 = 445.38 K
Finally, to convert this back to Celsius, subtract 273.15: T2(C) = 445.38 K - 273.15 = 172.23°C
The temperature at which the volume of the gas increases to 2.55 L is 172.23°C.