Three cylinders contain hydrogen, oxygen and carbon dioxide respectively under the following conditions: (H2= 5 liters, 2500 mmHg, 20 °C), (O2= 2 liters, 2 bar, 293 K), (CO2= 0.006 m3 , 3 atm, 20 °C). 1)Calculate the number of moles and the mass of each gas assuming them to be ideal. 2)The containers are connected by pipes of negligible volume. Calculate the total pressure. Calculate for each gas, the mass fraction, the molar fraction and the partial pressure.

Sure, let's solve this step by step:

1. To calculate the number of moles of each gas, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.

For hydrogen (H2): P = 2500 mmHg = 3.28 atm (1 atm = 760 mmHg) V = 5 liters = 0.005 m3 (1 m3 = 1000 liters) T = 20 °C = 293.15 K (K = °C + 273.15) R = 0.0821 atm.m3/(mol.K) (universal gas constant) n = PV/RT = (3.28 * 0.005) / (0.0821 * 293.15) = 0.0007 mol The molar mass of H2 = 2 g/mol, so the mass = n * molar mass = 0.0007 * 2 = 0.0014 g

For oxygen (O2): P = 2 bar = 1.97 atm (1 atm = 1.01325 bar) V = 2 liters = 0.002 m3 T = 293 K n = PV/RT = (1.97 * 0.002) / (0.0821 * 293) = 0.000082 mol The molar mass of O2 = 32 g/mol, so the mass = n * molar mass = 0.000082 * 32 = 0.0026 g

For carbon dioxide (CO2): P = 3 atm V = 0.006 m3 T = 20 °C = 293.15 K n = PV/RT = (3 * 0.006) / (0.0821 * 293.15) = 0.00074 mol The molar mass of CO2 = 44 g/mol, so the mass = n * molar mass = 0.00074 * 44 = 0.0326 g

2. The total pressure when the containers are connected can be calculated by adding the pressures of each gas. P_total = P_H2 + P_O2 + P_CO2 = 3.28 + 1.97 + 3 = 8.25 atm

The mass fraction of each gas is the mass of the gas divided by the total mass. The molar fraction is the number of moles of the gas divided by the total number of moles. The partial pressure is the molar fraction times the total pressure.

For H2: Mass fraction = 0.0014 / (0.0014 + 0.0026 + 0.0326) = 0.035 Molar fraction = 0.0007 / (0.0007 + 0.000082 + 0.00074) = 0.45 Partial pressure = 0.45 * 8.25 = 3.71 atm

For O2: Mass fraction = 0.0026 / (0.0014 + 0.0026 + 0.0326) = 0.065 Molar fraction = 0.000082 / (0.0007 + 0.000082 + 0.00074) = 0.05 Partial pressure = 0.05 * 8.25 = 0.41 atm

For CO2: Mass fraction = 0.0326 / (0.0014 + 0.0026 + 0.0326) = 0.9 Molar fraction = 0.00074 / (0.0007 + 0.000082 + 0.00074) = 0.5 Partial pressure = 0.5 * 8.25 = 4.13 atm

Please note that these are approximate values and the actual values may vary slightly due to rounding errors.