Final answer:
The molar mass of the unknown acid, HX, can be calculated using the distance at which the reaction product forms in the diffusion tube using Graham's law of effusion. The exact value can be found by setting up a proportion based on the distances from the sources of gases to the white ring.
Step-by-step explanation:
The question involves using Graham's law of effusion to determine the molar mass of an unknown acid, HX, using the distance a white ring forms in a tube when ammonia and the unknown acid are allowed to diffuse towards each other. Graham's law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. In this case, NH3 and HX react to form NH4X where the white ring is observed.
Since the position of the ring is 95.90 cm away from the flask of ammonia in a 140 cm tube, we can use the following proportion derived from Graham's law:
Rate of NH3 / Rate of HX = √(Molar Mass of HX) / √(Molar Mass of NH3)
Let's denote the distance from the HX flask to the ring as x. Since the total distance is 140 cm, x = 140 - 95.90 = 44.10 cm. We assume that the gases meet at a point where their rates of diffusion have covered distances inversely proportional to the square roots of their respective molar masses. This gives us:
(95.90 cm) / (44.10 cm) = √(Molar Mass of HX) / √(17.03 g/mol)
Solving for the molar mass of HX, we get:
Molar Mass of HX = [(95.90 / 44.10) ^ 2] * 17.03 g/mol
After calculating the exact value for the molar mass of HX, you can ascertain the identity of the unknown acid HX if it's among the common laboratory acids.