Question

CO₂ gas occupies a volume of 121 mL at 27°C and 1.05 atm, what temperature (in °C) is needed for CO₂ to occupy a volume of 293 mL at a pressure of 1.40 atm?

Answer 1

The temperature needed for CO₂ to occupy 293 mL at 1.40 atm, starting from 121 mL at 27°C and 1.05 atm, is calculated using the Combined Gas Law to be 127.4°C.

Step-by-step explanation:

The temperature required for CO₂ to occupy a volume of 293 mL at a pressure of 1.40 atm, given that it occupies 121 mL at 27°C and 1.05 atm, is 127.4°C.

To solve this, we need to use the Combined Gas Law, which is P1V1/T1 = P2V2/T2, where P is the pressure, V is the volume, and T is the temperature in Kelvin. First, we convert the initial and final temperatures to Kelvin (T1 = 27°C + 273.15 = 300.15 K, T2 = ?) and then rearrange the formula to solve for T2: T2 = (P2V2T1)/(P1V1).

Inserting the given values (P1 = 1.05 atm, V1 = 121 mL, T1 = 300.15 K, P2 = 1.40 atm, V2 = 293 mL), we get T2 = (1.40 atm * 293 mL * 300.15 K) / (1.05 atm * 121 mL), which calculates to 400.54 K. Convert back to Celsius by subtracting 273.15, yielding the final temperature T2 = 127.4°C.