Question

When two cotton plugs, one moistened with ammonia (17.03 g/mol) and the other with hydrochloric acid (36.46 g/mol), are simultaneously inserted into opposite ends of a glass tube that is 87.3 cm long, a white ring of NH4Cl forms where gaseous NH3 and gaseous HCl first come into contact. NH3(g) + HCl(g) → NH4Cl(s) at approximately what distance (in cm) from the ammonia-moistened plug does this occur? (Hint: Calculate the relative rates of diffusion for both NH3 and HCl, and find out how much faster NH3 diffuses than HCl. You can use the approximation used in section 8.7 that the distance traveled depends on the root mean square speed of each type of gas.)

Answer 1

To find the distance at which the white ring of NH4Cl forms in a glass tube when ammonia and hydrochloric acid come into contact, we can use Graham's law of diffusion. NH3 diffuses approximately 2.53 times faster than HCl, so the distance from the ammonia-moistened plug where the ring forms will be about 2.53 times the distance covered by HCl. The white ring forms at approximately 57.6 cm from the ammonia-moistened plug.

Step-by-step explanation:

To determine the distance from the ammonia-moistened plug where the white ring of NH4Cl forms, we need to calculate the relative rates of diffusion for NH3 and HCl. Graham's law of diffusion states that the rate of diffusion is inversely proportional to the square root of the molar mass. The molar mass of NH3 is 17.03 g/mol and the molar mass of HCl is 36.46 g/mol. By taking the square roots of their molar masses, we can calculate their relative rates of diffusion. NH3 diffuses approximately 2.53 times faster than HCl.

Since the distance traveled depends on the root mean square speed of each gas, and the ratio of diffusion rates is 2.53, the distance from the ammonia-moistened plug where the white ring forms will be approximately 2.53 times the distance covered by HCl. The total length of the glass tube is 87.3 cm, so to find the distance at which the white ring forms, we can use the following equation: Distance of the white ring = (2.53 / (2.53 + 1)) * 87.3 cm = 57.6 cm.