0.5 mole of oxygen,0.5 mole of nitrogen &0.25 mole of CO2 are mixed in a container of volume 5 litre at 27degree,wat is the pressure exerted

To find the pressure exerted by a mixture of gases in a container, we can use the ideal gas law, which is expressed as PV = nRT. In this equation, P represents pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin. Let's break this down step by step.

Step 1: Convert Temperature to Kelvin

The temperature given is 27 degrees Celsius. To convert this to Kelvin, we add 273.15:

T(K) = 27 + 273.15 = 300.15 K

Step 2: Calculate Total Moles of Gas

Next, we need to find the total number of moles of gas in the mixture. We have:

• 0.5 moles of oxygen (O2)
• 0.5 moles of nitrogen (N2)
• 0.25 moles of carbon dioxide (CO2)

Adding these together gives:

Total moles (n) = 0.5 + 0.5 + 0.25 = 1.25 moles

Step 3: Use the Ideal Gas Law

Now we can substitute the values into the ideal gas law. The volume (V) of the container is given as 5 liters, and the ideal gas constant (R) is typically 0.0821 L·atm/(K·mol) when using liters and atmospheres.

Now, substituting the values into the equation:

P = nRT / V

P = (1.25 moles) * (0.0821 L·atm/(K·mol)) * (300.15 K) / (5 L)

Step 4: Calculate the Pressure

Now, let's perform the calculation:

P = (1.25 * 0.0821 * 300.15) / 5

P = (30.703125) / 5

P = 6.140625 atm

Final Result

Therefore, the pressure exerted by the mixture of gases in the container is approximately 6.14 atm.

This calculation illustrates how the ideal gas law can be applied to determine the pressure of a gas mixture under specific conditions. Understanding these principles is essential in fields like chemistry and engineering, where gas behavior is a fundamental concept.