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Bot GPT 3.5 To calculate the new pressure after adding 4.00 mil of gas to the tank, we can use the ideal gas law:
\(PV = nRT\)
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
Since the tank is rigid, the volume remains constant. Therefore, the ratio of initial moles to final moles is equal to the ratio of initial pressure to final pressure:
\(\frac{P_1}{P_2} = \frac{n_1}{n_2}\)
Given:
\(P_1 = 772 kPa\)
\(V = 2.91 mil\)
\(n_1 = \frac{P_1V}{RT}\)
We can find \(n_1\) by rearranging the ideal gas law to solve for moles:
\(n_1 = \frac{P_1V}{RT} = \frac{(772 \times 2.91)}{(8.31 \times 293)} = 0.7517\)
After adding 4.00 mil of gas to the tank, the total number of moles becomes:
\(n_2 = n_1 + 4.00\)
Therefore, the final pressure can be calculated as:
\(P_2 = \frac{n_2}{n_1} \times P_1 = \frac{(0.7517 + 4.00)}{0.7517} \times 772 = 4903.1 kPa\)
Thus, the pressure after adding 4.00 mil of gas to the tank is 4903.1 kPa.