Question

A box of volume v and temperature t contains a mixture of two ideal gasses a and b, whose molecules have masses ma and mb, respectively. suppose there are n molecules of each type at the beginning of an experiment. each molecule of a combines with a molecule of b to form a new molecule c of mass ma mb. the experiment runs until all of a and b are converted to c.

a, what is the ratio of the pressure after the reaction to the pressure before (assuming no change in temperature)?

Answer 1

The ratio of the pressure after the reaction to the pressure before the reaction of ideal gases A and B forming gas C is 0.5 or 1/2, assuming constant temperature and volume.

Step-by-step explanation:

When ideal gases react to form a new gas, we can use the ideal gas law and Avogadro's Law to understand the changes in pressure. Given that molecules of gases A and B combine in a 1:1 ratio to form molecules of gas C, and that we begin with equal numbers of molecules of A and B (n of each), the number of molecules after the reaction is n (since each C molecule requires one A and one B).

Before the reaction, the total number of gas particles (molecules of A + molecules of B) is 2n. After the reaction, the number of gas molecules is n (since each molecule of C has one molecule from A and one from B). If the temperature and volume are kept constant, and using the fact that pressure is proportional to the number of gas particles (by the ideal gas law), the pressure after the reaction (Pafter) to the pressure before the reaction (Pbefore) is half:

Pafter/Pbefore = n/2n = ½ or 0.5