A gas mixture contains 50% helium and 50% methane by volume. What is the percent by \ weight of methane in the mixture?

To answer this question, we need to know the densities of helium and methane. The density of helium is about 0.1785 grams per liter and the density of methane is about 0.716 grams per liter.

1. First, let's assume we have 1 liter of the gas mixture. This means we have 0.5 liters of helium and 0.5 liters of methane.

2. Next, we calculate the weight of each gas in the mixture. The weight of helium is 0.5 liters * 0.1785 grams/liter = 0.08925 grams. The weight of methane is 0.5 liters * 0.716 grams/liter = 0.358 grams.

3. Now, we calculate the total weight of the gas mixture, which is the sum of the weight of helium and methane. The total weight is 0.08925 grams + 0.358 grams = 0.44725 grams.

4. Finally, we calculate the percent by weight of methane in the mixture. The percent by weight of methane is (weight of methane / total weight) * 100%. So, the percent by weight of methane is (0.358 grams / 0.44725 grams) * 100% = 80.02%.

So, the percent by weight of methane in the mixture is approximately 80.02%.