Phosphine, PH3PH3 , is a colorless, toxic gas that is used in the production of semiconductors as well as in the farming industry. When heated, phosphine decomposes into phosphorus and hydrogen gases. 4PH3(g)⟶P4(g)+6H2(g)4PH3(g)⟶P4(g)+6 H2(g) This decomposition is first order with respect to phosphine, and has a half‑life of 35.0 s at 953 K. Calculate the partial pressure of hydrogen gas that is present after 79.4 s79.4 s if a 4.60 L4.60 L vessel containing 2.57 atm2.57 atm of phosphine gas is heated to 953 K

Explanation:

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In this case, given the reaction:

We can represent the first-order reaction rate as:

Whose integration turns out:

In such a way, we can compute the initial concentration by using the ideal gas equation and the given pressure and temperature:

Next, by knowing the half-life, we can also compute the rate constant:

Thus, we can find the concentration after 79.4 s have passed by solving for the concentration of phosphine from the integrated rate law:

Then, we can compute the consumed moles phosphine by using he container's volume and the initial and final concentrations:

Hence, we compute the yielded moles of hydrogen by stoichiometry (4:6 molar ratio):

Finally, we compute the partial pressure of hydrogen with the previously computed moles of hydrogen by using the ideal gas equation:

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