How many moles of gas (to 1 decimal place, input value only), are contained in a 54.25 L vessel at a pressure of 173.6 kPa and temperature of 0.2 °C?

To solve this problem, we will use the ideal gas law equation, which is PV = nRT.

Where: P = pressure V = volume n = number of moles R = ideal gas constant T = temperature

Given: P = 173.6 kPa V = 54.25 L T = 0.2 °C

First, we need to convert the temperature from Celsius to Kelvin because the ideal gas law requires the temperature to be in Kelvin.

T(K) = T(°C) + 273.15 T(K) = 0.2 + 273.15 = 273.35 K

Next, we need to convert the pressure from kPa to atm because the ideal gas constant (R) we are using is in atm.

1 atm = 101.325 kPa P(atm) = P(kPa) / 101.325 P(atm) = 173.6 / 101.325 = 1.713 atm

Now we can plug the values into the ideal gas law equation. We are solving for n (number of moles), so we rearrange the equation to solve for n:

n = PV / RT

We use the value of R = 0.0821 L.atm/(mol.K) which is the ideal gas constant.

n = (1.713 atm * 54.25 L) / (0.0821 L.atm/(mol.K) * 273.35 K)

n = 2.8 moles

So, there are approximately 2.8 moles of gas in the vessel.