An ideal gas in contained in a cylinder with a volume of 5.0x102mL at a temperature of 30C and a pressure of 710 torr. The gas is then compressed to a volume of 25mL, and the temperature is raised to 820C. What is the new pressure of the gas?

(P1V1/T1)=(P2V2/T2)

thank u so much...

To solve this problem, we can use the combined gas law equation, which states that the initial pressure times the initial volume divided by the initial temperature is equal to the final pressure times the final volume divided by the final temperature:

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

First, we need to convert the initial conditions from Celsius to Kelvin. Celsius is converted to Kelvin by adding 273.15 to the Celsius temperature. So, the initial temperature is 30°C + 273.15 = 303.15 K.

Now, let's substitute the given values into the equation:

(710 torr * 500 mL) / 303.15 K = (P2 * 25 mL) / (820°C + 273.15 K)

Simplifying the equation:
(710 torr * 500 mL) / 303.15 K = (P2 * 25 mL) / 1093.15 K

Now, we can solve for P2, the new pressure:

(P2 * 25 mL) = (710 torr * 500 mL) * 1093.15 K / 303.15 K
P2 = (710 torr * 500 mL * 1093.15 K) / (303.15 K * 25 mL)

Calculating the values:
P2 = 13,399,646.88 / 7578.6
P2 ≈ 1767.85 torr

Therefore, the new pressure of the gas is approximately 1767.85 torr.

To solve this problem, we can use the combined gas law equation, which states that the product of the initial pressure and volume divided by the initial temperature is equal to the product of the final pressure and volume divided by the final temperature.

The equation for the combined gas law is:
(P1 * V1) / T1 = (P2 * V2) / T2

First, let's convert the given values to the appropriate units:
Initial volume (V1) = 5.0 x 10^2 mL = 5.0 x 10^-1 L
Initial temperature (T1) = 30°C = 273.15 + 30 = 303.15 K
Initial pressure (P1) = 710 torr

Final volume (V2) = 25 mL = 2.5 x 10^-2 L
Final temperature (T2) = 820°C = 273.15 + 820 = 1093.15 K

Now we can plug the values into the combined gas law equation:

(710 torr * 5.0 x 10^-1 L) / 303.15 K = (P2 * 2.5 x 10^-2 L) / 1093.15 K

Next, we can rearrange the equation to solve for P2 (the new pressure):

P2 = (710 torr * 5.0 x 10^-1 L * 1093.15 K) / (2.5 x 10^-2 L * 303.15 K)

Simplifying the equation:
P2 = (355 torr * 1093.15 K) / 7.582375 K

P2 = 51362.825 / 7.582375

P2 ≈ 6779.4 torr

Therefore, the new pressure of the gas is approximately 6779.4 torr.