The figure shows a pV diagram for 8.3 g of nitrogen gas (N₂)in a sealed container.The temperature T₁ of the gas in state 1 is 79°C.What are (a)the pressure p₁ of the gas in state 1 and (b)the temperature T₂ of the gas in state 2? The ideal gas constant is R = 8.314 J/mol ∙ K = ,and the ATOMIC weight of nitrogen is 14 g/mol. A)(a)86 atm,(b)700°C. B)(a)19 atm,(b)700°C. C)(a)86 atm,(b)160°C. D)(a)19 atm,(b)160°C.

Question

Quizplus · Accepted Answer

(a) The pressure at state 1 can be obtained from the graph as the corresponding pressure value on the y-axis. Reading from the graph, the pressure at state 1 is approximately 86 atm.
(b) To find the temperature at state 2, we can use the ideal gas law:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. Since the container is sealed, the volume remains constant. We can also find the number of moles of nitrogen gas using its mass and molar mass:
n = m/M = 8.3 g / 28 g/mol = 0.297 mol
Substituting these values into the ideal gas law and solving for T2, we get:
T2 = (P2V) / (nR)
At state 2, the pressure and volume can be read from the graph as approximately 19 atm and 4 L, respectively. Substituting these values and solving for T2, we get:
T2 = (19 atm * 4 L) / (0.297 mol * 8.314 J/mol*K) = 973 K
Converting this to Celsius, we get:
T2 = 700°C.

The Figure Shows a PV Diagram for 8