To find the new pressure, we can use the combined gas law, which states that the ratio of the initial pressure to the final pressure is equal to the ratio of the initial volume to the final volume, multiplied by the ratio of the final temperature to the initial temperature.
Mathematically, the combined gas law can be expressed as:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure (1.2 atm)
V1 = initial volume (0.350 L)
T1 = initial temperature (22.0 degrees Celsius + 273.15) -> converted to Kelvin
P2 = final pressure (unknown)
V2 = final volume (0.050 L)
T2 = final temperature (22.0 degrees Celsius + 25 degrees Celsius + 273.15) -> converted to Kelvin
Let's plug in the values and solve for P2:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
(1.2 atm * 0.350 L) / (22.0 + 273.15 K) = (P2 * 0.050 L) / (22.0 + 25 + 273.15 K)
Simplifying the equation:
0.42 / 295.15 = (P2 * 0.050) / 320.15
Cross-multiplying:
0.42 * 320.15 = P2 * 0.050
Solving for P2:
P2 = (0.42 * 320.15) / 0.050
P2 ≈ 2.691 atm
Therefore, the new pressure that will hold the same sample of gas in a volume of 0.050 L when the temperature increases by 25 degrees Celsius is approximately 2.691 atm.