A closed gas cylinder contains 0.500 mole H2, 0.300 mole O2, 1.200 mole CO2 at a temperature of 25 °C and a pressure of 2.00 atm

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To find the total pressure inside the gas cylinder, we can use Dalton's law of partial pressure.

According to Dalton's law, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of each individual gas.

In this case, we have three different gases: H2, O2, and CO2. The partial pressure of each gas can be calculated using 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 ideal gas constant, and T is the temperature in Kelvin.

Here's how we can calculate the partial pressure of each gas:

1. Convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 25 + 273.15 = 298.15 K

2. Calculate the partial pressure of each gas using the ideal gas law:
For H2:
PH2 = (nH2 * R * T) / V
PH2 = (0.500 * 0.0821 * 298.15) / V

For O2:
PO2 = (nO2 * R * T) / V
PO2 = (0.300 * 0.0821 * 298.15) / V

For CO2:
PCO2 = (nCO2 * R * T) / V
PCO2 = (1.200 * 0.0821 * 298.15) / V

3. Calculate the total pressure:
PT = PH2 + PO2 + PCO2

Note: The ideal gas constant, R, has a value of 0.0821 L·atm/(mol·K).

You can substitute the given values for the number of moles and temperature into the equations and solve to find the partial pressure of each gas. Finally, sum up the partial pressures to get the total pressure inside the gas cylinder.