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If an 80.0 L cylinder is filled with 4.00 g of [tex]N_2[/tex], 6.00 g of [tex]O_2[/tex], and 8.00 g of [tex]CO_2[/tex] at a temperature of 600 K, what is the total pressure inside the cylinder?

Answer :

To find the total pressure inside the cylinder, we need to use the ideal gas law equation, which is given by: PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.


First, we need to calculate the total number of moles of gas in the cylinder. To do this, we divide the mass of each gas by its molar mass.
The molar mass of N2 is 28.0134 g/mol, so the number of moles of N2 is 4.00 g / 28.0134 g/mol = 0.143 moles.
The molar mass of O2 is 31.9988 g/mol, so the number of moles of O2 is 6.00 g / 31.9988 g/mol = 0.188 moles.
The molar mass of CO2 is 44.0095 g/mol, so the number of moles of CO2 is 8.00 g / 44.0095 g/mol = 0.182 moles.
Next, we need to calculate the total number of moles of gas in the cylinder by adding the number of moles of each gas together:
Total moles of gas = 0.143 moles + 0.188 moles + 0.182 moles = 0.513 moles.

Now, we can substitute the values into the ideal gas law equation to find the pressure:
P * 80.0 L = 0.513 moles * 0.0821 L/mol*K * 600 K
Simplifying the equation:
P = (0.513 moles * 0.0821 L/mol*K * 600 K) / 80.0 L
Calculating the expression:
P = 2.434 atm
Therefore, the total pressure inside the cylinder is 2.434 atm.

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