On passing 2 litres of a mixture of CO and CO2 over red hot charcoal, the volume becomes 2.5 litres. The volume fraction of Co in the mixture is
So, some of the CO2 became CO.
CO2+ C> 2CO
If you assume all the CO2 was converted, then the the added volume of .5 liters equals the new CO, minus the original CO2
2.5litersCO= xlitersCOoriainal+ 2(2-x)liters CO new.
2.5=x+4-2x if my algebra is right, so
-1.5=-x
or the original amount of CO was 1.5, or 3/4 of the original mixture was CO.
To find the volume fraction of CO (carbon monoxide) in the mixture, we need to analyze the change in volume after passing the mixture over red hot charcoal.
Let's assume that the initial volume of CO in the mixture is V1, and the initial volume of CO2 (carbon dioxide) is V2. Therefore, we have the following information:
Initial volume of the mixture (V_initial) = V1 + V2 = 2 liters
Final volume of the mixture after passing over charcoal (V_final) = 2.5 liters
To find the volume fraction of CO, we need to understand that the volume change is caused by the conversion of CO2 to CO. The carbon dioxide (CO2) reacts with charcoal (C) to form carbon monoxide (CO) according to the following balanced chemical equation:
CO2 + C → 2CO
From this equation, we can infer that each mole of CO2 reacts to form 2 moles of CO. This means that the moles of CO formed are equal to twice the moles of CO2 consumed.
Now, let's assume that the initial moles of CO2 in the mixture are n2. Therefore, the moles of CO formed will be 2n2.
Since volume is directly proportional to the number of moles of a gas at a constant temperature and pressure, we can express the volume relationship using the ideal gas law equation:
V1/V2 = n1/n2
Where V1 and V2 are the initial and final volumes, and n1 and n2 are the initial and final moles, respectively.
Substituting the values we have, we get:
2/2.5 = (V1 + V2)/(V2 + 2V2)
Simplifying the equation:
2/2.5 = (2)/(3V2)
Cross-multiplying:
4 = 5V2
V2 = 4/5 = 0.8 liters
Now, we know the volume of CO2 in the mixture is 0.8 liters. To find the volume fraction of CO, we need to subtract this volume from the initial volume of the mixture:
V1 - V2 = 2 - 0.8 = 1.2 liters
Finally, the volume fraction of CO in the mixture is:
Volume fraction of CO = (Volume of CO)/(Total volume of the mixture) = V1 / (V1 + V2) = 1.2 / (1.2 + 0.8) = 1.2/2 = 0.6 or 60%
Therefore, the volume fraction of CO in the mixture is 60%.