Answer :
Final answer:
The new temperature of nitrogen gas after expansion is approximately 726.9 oC.
Explanation:
To calculate the new temperature of nitrogen gas after expansion, we can use the equation (P1 * V1) / T1 = (P2 * V2) / T2, where P1, V1, and T1 are the initial pressure, volume, and temperature, and P2, V2, and T2 are the final pressure, volume, and temperature.
Given:
- Initial volume (V1) = 390 mL
- Initial temperature (T1) = 36.9 oC
- Initial pressure (P1) = 657 torr
- Final volume (V2) = 870 mL
- Final pressure (P2) = 570 torr
First, we need to convert the temperatures to Kelvin. The Kelvin temperature scale is used in gas law calculations.
Initial temperature in Kelvin (T1) = 36.9 + 273.15 = 309.05 K
Using the equation, we can solve for the final temperature (T2):
(P1 * V1) / T1 = (P2 * V2) / T2
Substituting the given values:
(657 torr * 390 mL) / 309.05 K = (570 torr * 870 mL) / T2
Simplifying the equation:
255,630 torr * mL / K = 495,900 torr * mL / T2
Cross-multiplying:
255,630 torr * mL * T2 = 495,900 torr * mL * 309.05 K
Dividing both sides by 255,630 torr * mL:
T2 = (495,900 torr * mL * 309.05 K) / (255,630 torr * mL)
Canceling out the units:
T2 = 1,000.05 K
Finally, we need to convert the temperature back to Celsius:
T2 in Celsius = 1,000.05 K - 273.15 = 726.9 oC
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