To **choose the rate law** that describes this reaction.

**4PH**_{3(}g) →P_{4}(g) + 6H_{2}**(g) **

**Step 1**: ICE Chart

at t = 0, P_{tot} = P_{PH3}

**Step 2**: Solve for x for t = 40.0 and t = 80.0 (for comparison)

Based on Dalton’s Law, the** total pressure** is the sum of the partial pressure of the individual gases.

$\overline{){{\mathbf{P}}}_{{\mathbf{total}}}{\mathbf{=}}{{\mathbf{P}}}_{\mathbf{Gas}\mathbf{}\mathbf{1}}{\mathbf{+}}{{\mathbf{P}}}_{\mathbf{Gas}\mathbf{}\mathbf{2}}{\mathbf{+}}{{\mathbf{P}}}_{\mathbf{Gas}\mathbf{}\mathbf{3}}{\mathbf{+}}{\mathbf{}}{\mathbf{.}}{\mathbf{.}}{\mathbf{.}}}$

t = 40.0 mins:

**P _{tot} = P_{PH3} + P_{P4} + P_{H2}**

**151 = 100 - 4x + x + 6x **

**3x = 151 - 100**

**x = 17 torr**

*after 40 mins:*

**P _{PH3} ** = 100 - 4(17)

** P_{PH3 }**= 32 torr

t = 80.0 mins:

**P _{tot} = P_{PH3} + P_{P4} + P_{H2}**

**168 = 100 - 4x + x + 6x **

**3x = 168 - 100**

**x = 22.67 torr**

*after 80 mins:*

**P _{PH3} ** = 100 - 4(17)

** P_{PH3 }**= 9.33 torr

**Step 3: Check if 1st order reaction: rate = k[PH _{3}] **

**exponent***of reactant =***order**of reaction (if 1, not written)**k**_{t=40 }= k_{t=80}

** integrated rate law** for a first-order reaction:

$\overline{){\mathbf{ln}}{{\mathbf{P}}}_{{\mathbf{t}}}{\mathbf{=}}{\mathbf{-}}{\mathbf{kt}}{\mathbf{+}}{{\mathbf{lnP}}}_{{\mathbf{0}}}}$

**Solve for k** at t = 40.0 mins:

$\mathbf{ln}\mathbf{\left(}\mathbf{32}\mathbf{\right)}\mathbf{=}\mathbf{-}\mathbf{k}\mathbf{(}\mathbf{40}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{min}\mathbf{)}\mathbf{+}\mathbf{ln}\mathbf{\left(}\mathbf{100}\mathbf{\right)}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathbf{ln}\mathbf{\left(}\mathbf{32}\mathbf{\right)}\mathbf{-}\mathbf{ln}\mathbf{\left(}\mathbf{100}\mathbf{\right)}\mathbf{=}\mathbf{-}\mathbf{k}\mathbf{(}\mathbf{40}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{min}\mathbf{)}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\frac{\overline{)\mathbf{-}}\mathbf{1}\mathbf{.}\mathbf{1394}}{\overline{)\mathbf{-}}\mathbf{40}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{min}}\mathbf{=}\frac{\overline{)\mathbf{-}}\mathbf{k}\mathbf{\left(}\overline{)\mathbf{40}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{min}}\mathbf{\right)}}{\overline{)\mathbf{-}}\overline{)\mathbf{40}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{min}}}$

Phosphine, PH3(g), decomposes according to the equation

4PH_{3(}g) →P_{4}(g) + 6H_{2}(g)

Time (min) P_{total }(Torr)

0.00 100

40.0 151

80.0 168

100 171

The kinetics of the decomposition of phosphine at 950 K was followed by measuring the total pressure in the system as a function of time. The data to the right were obtained in a run where the reaction chamber contained only pure phosphine at the start of the reaction.

Choose the rate law that describes this reaction.

a) rate = k(P_{PH}_{3})^{2}^{ }

b) rate = k(P_{PH}_{3})^{-2}

c) rate = k

d) rate = k(P_{PH}_{3})

e) rate = k(P_{PH}_{3})^{-1}

Calculate the value of the rate constant and choose the correct units

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