What is the volume of 1 mole of a gas mixture at 25 ° C and 0.1 MPa?12.25 dm322.41 dm324.5 dm349 dm373.5 dm3
Question
What is the volume of 1 mole of a gas mixture at 25 ° C and 0.1 MPa?12.25 dm322.41 dm324.5 dm349 dm373.5 dm3
Solution
The volume of one mole of any gas at standard temperature and pressure (STP) is 22.4 dm^3. However, the conditions specified in the question are not standard conditions.
The ideal gas law, PV=nRT, can be used to find the volume of the gas under these conditions.
In this equation: 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, convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature. So, 25 °C = 298.15 K.
Next, convert the pressure from MPa to Pa by multiplying by 1,000,000. So, 0.1 MPa = 100,000 Pa.
The value of R depends on the units used. In this case, since we are using Pa for pressure, dm^3 for volume, mol for the number of moles, and K for temperature, we should use R = 8.3145 Pa·dm^3/mol·K.
Now, we can substitute the known values into the ideal gas law and solve for V:
V = nRT/P V = (1 mol)(8.3145 Pa·dm^3/mol·K)(298.15 K) / 100,000 Pa V = 24.789 dm^3
So, the volume of the gas under these conditions is approximately 24.789 dm^3. The closest answer choice to this value is 24.5 dm^3.
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