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At a certain temperature it takes 11.2 s for 1.78 3 1023 mol of NH3 gas to effuse through a pinhole. Under the same conditions, how long will it take for the same amount of phosphine gas, PH3, to effuse through the same pinhole?

Short Answer

Expert verified
Answer: It takes approximately 7.92 seconds for the same amount of phosphine gas (PH3) to effuse through the same pinhole under the same conditions.

Step by step solution

01

Calculate the molar masses of NH3 and PH3

Since we need to find the ratio of molar masses, we need to determine the molar mass of each gas. The molar mass of NH3 is the sum of the molar mass of nitrogen and three times the molar mass of hydrogen. M_NH3 = M_N + 3 x M_H = (1 x 14) + (3 x 1) = 17 g/mol Similarly, the molar mass of PH3 is the sum of the molar mass of phosphorus and three times the molar mass of hydrogen. M_PH3 = M_P + 3 x M_H = (1 x 31) + (3 x 1) = 34 g/mol
02

Apply Graham's Law to calculate the time required for PH3 to effuse

Now that we have the molar masses, we can plug them into the equation derived from Graham's Law in terms of time: t1 / t2 = sqrt(M_PH3 / M_NH3) Given that t1 = 11.2 s, we can now solve for t2: t2 = t1 * sqrt(M_NH3 / M_PH3) = 11.2 * sqrt(17 / 34) t2 = 11.2 * sqrt(0.5) ≈ 7.92 s
03

Round the result to an appropriate number of significant figures

As the given data in the problem is only provided with 3 significant figures, we should round our answer to 3 significant figures as well: t2 ≈ 7.92 s Therefore, it will take approximately 7.92 seconds for the same amount of phosphine gas, PH3, to effuse through the same pinhole under the same conditions.

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Most popular questions from this chapter

Consider three sealed tanks all at the same temperature, pressure, and volume. Tank A contains \(\mathrm{SO}_{2}\) gas. Tank B contains \(\mathrm{O}_{2}\) gas. Tank C contains \(\mathrm{CH}_{4}\) gas. Use LT (for "is less than"), GT (for "is greater than"), EQ (for "is equal to"), or MI (for " more information required") as answers to the blanks below. (a) The mass of \(\mathrm{SO}_{2}\) in tank \(\mathrm{A}\) the mass of \(\mathrm{O}_{2}\) in \(\operatorname{tank} \mathrm{B}\). (b) The average translational energy of \(\mathrm{CH}_{4}\) in \(\operatorname{tank} \mathrm{C}\) the average translational energy of \(\mathrm{SO}_{2}\) in \(\operatorname{tank} \mathrm{A}\) (c) It takes \(20 \mathrm{~s}\) for all of the \(\mathrm{O}_{2}\) gas in tank \(\mathrm{B}\) to effuse out of a pinhole in the tank. The time it takes for all of the \(\mathrm{SO}_{2}\) to effuse out of tank A from an identical pinhole \(40 \mathrm{~s}\) (d) The density of \(\mathrm{O}_{2}\) in tank \(\mathrm{B} \longrightarrow\) the density of \(\mathrm{CH}_{4}\) in tank C. (e) The temperature in tank \(\mathrm{A}\) is increased from \(150 \mathrm{~K}\) to \(300 \mathrm{~K}\). The temperature in tank \(\mathrm{B}\) is kept at \(150 \mathrm{~K}\). The pressure in tank \(\mathrm{A}\) is half the pressure in \(\operatorname{tank}\) B.

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