Answer to Question #109094 in Chemistry for Joy

Question

1.Ammonia difuses 1.41times as fast as gas xH3 . determine the relative atomic mass of element x
2.A sealed gas tube containing air at stp was immersed in water at 100c . assuming there was no increase in the volume of the glass tube due to expansion of gas, calculate the pressure of the air inside the tube

Answer 1

1. According to the Graham's law of diffusion, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass:

$\frac{Rate_{NH_3}}{Rate_{XH_3}} = \sqrt{\frac{M_{XH_3}}{M_{NH_3}}}$ . The molar mass of ammonia is 17.031 g/mol, and the ratio of rates is 1.41:

$1.41 = \sqrt{\frac{M_{XH_3}}{17.031}}$

Therefore, the molar mass of XH₃ gas is:

$1.41^2\cdot17.031 = 33.86$ g/mol. The relative atomic mass of the element X is the molar mass of XH₃ minus the relative atomic mass of three hydrogen atoms (1.01):

$33.86 - 3.02 = 30.84$. This relative atomic mass is very close to the atomic mass of phosphorus, P.

2. Assuming that air is the ideal gas, we can apply the Charle's law in this case. Remember that we should convert celsius to kelvin (+273.15). According to the Charle's law:

$\frac{p_{stp}}{T_{stp}} = \frac{p_{x}}{100+273.15}$

New pressure $p_x$ is:

$p_x = \frac{373.15 K\cdot 10^5 Pa}{273.15 K} = 1.37\cdot10^5$ Pa

Answer: 1. The relative atomic mass of X element is 30.8. 2. The new pressure inside the tube is 1.37·10⁵ Pa.