Final answer:
Using the Combined Gas Law, the final pressure of the gas when the temperature is increased to 400 K and the volume is compressed to 10 mL will be 2.8 atm.
Step-by-step explanation:
To solve this problem, we will apply the Combined Gas Law, which combines Charles's, Boyle's, and Gay-Lussac's Laws all together. The law can be expressed as (P1 * V1) / T1 = (P2 * V2) / T2, where P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes, and T1 and T2 are the initial and final temperatures in Kelvin.
Given:
Initial pressure (P1): 2.1 atm
Initial volume (V1): 25 mL
Initial temperature (T1): 300 K
Final temperature (T2): 400 K
Final volume (V2): 10 mL
To find the final pressure (P2), we can rearrange the Combined Gas Law formula to solve for P2:
P2 = (P1 * V1 * T2) / (T1 * V2)
Plugging in the given values, we get:
P2 = (2.1 atm * 25 mL * 400 K) / (300 K * 10 mL)
P2 = 2.8 atm
Therefore, if you increase the temperature to 400 K and compress the gas to a volume of 10 mL, the pressure will be 2.8 atm.