Sure, I'd be happy to help you solve this problem! Gas law problems can be challenging, but let's go through the solution step by step.
The first step is to understand the given information. We have a 6 L cylinder containing four gases: CO2, H2, CO, and H2O. We are given their respective partial pressures: CO2 = 63.1 atm, H2 = 21.1 atm, CO = 84.2 atm, and H2O = 31.6 atm. We need to find the number of grams of CO2 in the cylinder.
To solve this problem, we will use the ideal gas law equation: PV = nRT. This equation relates the pressure (P), volume (V), number of moles (n), gas constant (R), and temperature (T) of a gas.
To find the number of moles of CO2, we need to rearrange the ideal gas law equation:
n = PV / RT
where n is the number of moles of gas, P is the pressure, V is the volume, R is the gas constant, and T is the temperature in Kelvin.
However, before we proceed, we need to convert the temperature from Celsius to Kelvin. The temperature in Kelvin (T) is equal to the temperature in Celsius (T°C) plus 273.15.
Given that the temperature is 100 °C, we can convert it to Kelvin:
T = 100 °C + 273.15 = 373.15 K
Now, let's calculate the number of moles of CO2:
n(CO2) = (CO2 pressure) x (cylinder volume) / (gas constant) x (temperature)
n(CO2) = (63.1 atm) x (6 L) / (0.0821 L·atm/mol·K) x (373.15 K)
Calculating this expression gives us the number of moles of CO2 present in the cylinder.