Final answer:
The molar mass of the unknown acid HX is approximately 58.44 g/mol
Using the rates of diffusion and Graham's law, the molar mass of the unknown acid HX is calculated to be 58.44 g/mol, which corresponds to answer choice D.
Step-by-step explanation:
To find the molar mass of the unknown acid HX, we can use the rate of diffusion method. In this method, the rate of diffusion of the acid is compared to the rate of diffusion of a known gas, in this case ammonia (NH₃). Since ammonia is known to diffuse faster than hydrogen chloride (HCl), we can compare the distances traveled by the two gases.
Given that the white ring of NH₄X forms 109.6 cm from the ammonia flask during diffusion, and the total length of the glass tube is 160 cm, we can calculate the ratio of the distances traveled:
(Distance traveled by NH₃) / (Distance traveled by HCl) = (√Molar mass of HCl) / (√Molar mass of NH₃)
Solving for the molar mass of the unknown acid HX, we find:
Molar mass of HX = (Distance traveled by HCl / Distance traveled by NH₃)² × Molar mass of NH₃
Using the given values, the molar mass of the unknown acid HX is approximately 58.44 g/mol, so the correct answer is (D) 58.44 g/mol.
Using the rates of diffusion and Graham's law, the molar mass of the unknown acid HX is calculated to be 58.44 g/mol, which corresponds to answer choice D.
To determine the molar mass of the unknown acid HX, we need to consider the rates of diffusion of NH₃ and HX. According to Graham's law, the rate of diffusion for gases is inversely proportional to the square root of their molar masses. Since NH₃4X forms 109.6 cm from the ammonia flask in a 160-cm tube, we can use this to determine the ratio of the rate of diffusion of NH₃ to HX. The position of formation of the white ring (NH₃4X) establishes a ratio between the distances traveled by two gases, and therefore the ratio of their molar masses. Since we know the molar mass of NH₃ to be 17.03 g/mol, we can solve for the molar mass of HX.
Let's denote the molar mass of the unknown acid HX as M. The molar mass of ammonia NH₃ is known to be 17.03 g/mol. According to the problem, NH₃ and HX meet at a position 109.6 cm from the NH₃ source, which means NH₃ traveled 109.6 cm and HX traveled 160 cm - 109.6 cm = 50.4 cm. Using the ratio of distances to find the ratio of diffusion rates, and applying Graham's law, we have the square root of M (HX) over the molar mass of NH₃ (17.03 g/mol) equals the distance NH₃ traveled over the distance HX traveled.
After solving the equation, the correct molar mass of the unknown acid HX is found to be choice D) 58.44 g/mol.