Answer: To find the value of x, we need to determine the proportions of the two gases in the mixture. We can do this by using the information provided about the total carbon and hydrogen content of the mixture.
First, we need to calculate the total mass of carbon and hydrogen in the mixture. We know that the mixture contains 87% carbon and 13% hydrogen, so the total mass of carbon is 87% * 41.4 g = 36.198 g. Similarly, the total mass of hydrogen is 13% * 41.4 g = 5.382 g.
Next, we can use the ideal gas law, which states that PV = nRT, to determine the number of moles of each gas in the mixture. Here, 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.
We know the pressure, volume, and temperature of the mixture, and we can use the atomic weights of carbon and hydrogen to calculate the number of moles of each gas. The atomic weight of carbon is 12.01 g/mol and the atomic weight of hydrogen is 1.008 g/mol.
Let's first find the number of moles of carbon in the mixture:
n(C) = (PV) / (RT)
= (1.56 atm * 10 L) / (0.08206 Latm/molK * (317.15 K))
= 0.1039 mol
Next, let's find the number of moles of hydrogen in the mixture:
n(H) = (PV) / (RT)
= (1.56 atm * 10 L) / (0.08206 Latm/molK * (317.15 K))
= 0.0161 mol
Finally, we can use the ratio of the number of moles of each gas to determine the value of x. We know that the gas mixture contains a total of 0.1039 mol of carbon and 0.0161 mol of hydrogen. The ratio of the number of moles of carbon to the number of moles of hydrogen is therefore 0.1039 mol / 0.0161 mol = 6.4.
Since we are looking for the value of x, we can express this ratio as CxH8 / CxH12. This gives us the equation:
(CxH8) / (CxH12) = 6.4
Solving this equation gives us x = 6.4, so the value of x is 6.4.
I hope this helps! Let me know if you have any questions.