A sample gas has a volume of 200 cm^3 at 25 degrees celsius and 700 mmHg. If the pressure is reduced to 280 mmHg, what volume would the gas occupy at the same temperature?

P1V1 = P2V2

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

(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.

Step 1: Convert the temperature from degrees Celsius to Kelvin
To convert from degrees Celsius to Kelvin, add 273.15 to the temperature in Celsius.
T1 = 25°C + 273.15 = 298.15 K

Step 2: Substitute the given values into the formula
(P1 * V1) / T1 = (P2 * V2) / T2

Given:
P1 = 700 mmHg
V1 = 200 cm^3
P2 = 280 mmHg
T1 = 298.15 K

We are looking for V2, so let's solve for it.

Step 3: Rearrange the formula to solve for V2
V2 = (P1 * V1 * T2) / (P2 * T1)

Step 4: Substitute the known values into the rearranged formula and solve for V2
V2 = (700 mmHg * 200 cm^3 * T2) / (280 mmHg * 298.15 K)

Step 5: Convert the pressure and volume to consistent units
To ensure the units are consistent, we need to convert mmHg to atm and cm^3 to liters.
1 mmHg = 0.00131578947 atm
1 cm^3 = 0.001 liters

V2 = (0.00131578947 atm * 0.2 liters * T2) / (0.00131578947 atm * 298.15 K)

Canceling out the units, we have:
V2 = (0.2 * T2) / 298.15

Therefore, the volume of the gas at the same temperature (T2) with a pressure of 280 mmHg is given by the equation:

V2 = (0.2 * T2) / 298.15