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$E=\frac 12mv^2$ is valid for translational kinetic energy and the speed of the centre of mass. Vibrational or rotational energy does not count, as an object may vibrate or rotate even if it's centre of mass has zero speed. As each translational degree of freedom has the mean energy $E=\frac 12kT$, the mean translational kinetic energy is $E_\mathrm{transl}... 4 According to the equipartition theorem, energy is shared equally among all accessible degress of freedom. A monatomic ideal gas has three translational degrees of freedom, so each translational degree of freedom has an energy of$\frac12 k T$, for a total translational energy of$\frac32 k T$. A diatomic ideal gas has three translational degrees of ... 1 This is clearly a homework question. Yet, since OP has given good effort to solve the question, I'd like to give OP some insight to solve these kinds of questions, taking current question as an example. Suppose the mixture contains$x\;\pu {g}$of$\ce{CH4}$and$y\;\pu {g}$of$\ce{C2H4}$. The combustion reactions of$\ce{CH4}$and$\ce{C2H4}\$ can be given ...