Hydrogen gas has a pressure of 765mm Hg, a volume of 355mL,and a temperature of 22 degrees C. What is the new volume of this gas if the pressure is 5.1atm,and at a temperature of 48degrees C?

To find the new volume of the gas, we can use the combined gas law equation. The combined gas law relates the initial and final states of a gas when one or more of the variables (pressure, volume, temperature) change. It can be written as:

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

Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure
V2 = final volume (what we are trying to find)
T2 = final temperature

Let's plug in the given values:

P1 = 765 mmHg (we need to convert it to atm)
V1 = 355 mL (we need to convert it to liters)
T1 = 22 °C (we need to convert it to Kelvin)

To convert mmHg to atm, divide by 760:
P1 = 765 mmHg / 760 mmHg/atm ≈ 1.00658 atm

To convert mL to liters, divide by 1000:
V1 = 355 mL / 1000 mL/L ≈ 0.355 L

To convert °C to Kelvin, add 273.15:
T1 = 22 °C + 273.15 ≈ 295.15 K

Now let's plug in the final values:

P2 = 5.1 atm
T2 = 48 °C + 273.15 ≈ 321.15 K

Now we can rearrange the equation to solve for V2:

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

V2 = (1.00658 atm * 0.355 L * 321.15 K) / (5.1 atm * 295.15 K)

V2 ≈ 0.0842 L

Therefore, the new volume of the hydrogen gas would be approximately 0.0842 liters.