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If 390 mL of nitrogen at 36.9 oC and 657 torr is

allowed to expand to 870 mL and 570 torr, what is the new

temperature in Celsius?

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

Learn more about calculating the new temperature of nitrogen gas after expansion here:

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