a sample of nitrogen gas occupies a volume of 20cm3 at 500k and 760mmhg what will it volume be at 860mmhg 400k

P1*V1/T1=P2*V2/T2

V2= P1*V1*T2/(T1*P2)

To determine the new volume of nitrogen gas, we can use the combined gas law, which relates the initial and final conditions of pressure, volume, and temperature.

The combined gas law equation is as follows:

(P1 * V1) / (T1) = (P2 * V2) / (T2)

Where:
P1 and P2 are the initial and final pressures, respectively.
V1 and V2 are the initial and final volumes, respectively.
T1 and T2 are the initial and final temperatures, respectively.

Let's plug in the given values into the equation:

P1 = 760 mmHg (initial pressure)
V1 = 20 cm^3 (initial volume)
T1 = 500 K (initial temperature)

P2 = 860 mmHg (final pressure)
V2 = ? (final volume)
T2 = 400 K (final temperature)

(760 mmHg * 20 cm^3) / 500 K = (860 mmHg * V2) / 400 K

Now, we can solve for V2 by rearranging the equation:

20 cm^3 / 500 K = V2 / 400 K

Cross-multiplying and rearranging further:

20 cm^3 * 400 K = 500 K * V2

8000 cm^3 * K = 500 K * V2

V2 = (8000 cm^3 * K) / 500 K

V2 = 16 cm^3

Therefore, the volume of nitrogen gas at a pressure of 860 mmHg and a temperature of 400 K will be 16 cm^3.