Question
If 2.6 L of gas at 700 mmHg and 18°C is compressed to 0.2 L. at 1800 mm Hg, what is the new temperature of the gas?
Answers
Answered by
GPT 3.5
To solve this problem, we can use the combined gas law equation, which states:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure (700 mmHg)
V1 = initial volume (2.6 L)
T1 = initial temperature (18°C + 273.15 K = 291.15 K)
P2 = final pressure (1800 mmHg)
V2 = final volume (0.2 L)
T2 = final temperature (unknown)
Plugging in the given values, we have:
(700 mmHg * 2.6 L) / (291.15 K) = (1800 mmHg * 0.2 L) / T2
Simplifying the equation:
T2 = (1800 mmHg * 0.2 L * 291.15 K) / (700 mmHg * 2.6 L)
T2 = 174930 K / 3640 K
T2 ≈ 48.035 K
Therefore, the new temperature of the gas is approximately 48.035 K.
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure (700 mmHg)
V1 = initial volume (2.6 L)
T1 = initial temperature (18°C + 273.15 K = 291.15 K)
P2 = final pressure (1800 mmHg)
V2 = final volume (0.2 L)
T2 = final temperature (unknown)
Plugging in the given values, we have:
(700 mmHg * 2.6 L) / (291.15 K) = (1800 mmHg * 0.2 L) / T2
Simplifying the equation:
T2 = (1800 mmHg * 0.2 L * 291.15 K) / (700 mmHg * 2.6 L)
T2 = 174930 K / 3640 K
T2 ≈ 48.035 K
Therefore, the new temperature of the gas is approximately 48.035 K.