Problem: Phosphine, PH3(g), decomposes according to the equation4PH3(g) →P4(g) + 6H2(g) Time (min)        Ptotal (Torr) 0.00                  10040.0                   15180.0                   168100                     171The 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(PPH3)2 b) rate = k(PPH3)-2c) rate = kd) rate = k(PPH3)e) rate = k(PPH3)-1Calculate the value of the rate constant and choose the correct units

FREE Expert Solution

To choose the rate law that describes this reaction.

4PH3(g) →P4(g) + 6H2(g) 


Step 1: ICE Chart


at t = 0, Ptot  = PPH3


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.


Ptotal=PGas 1+PGas 2+PGas 3+ ...


t = 40.0 mins:

Ptot = PPH3 + PP4 + PH2

151 = 100 - 4x + x + 6x 

3x = 151 - 100

x = 17 torr

after 40 mins:

PPH3  = 100 - 4(17) 

PPH= 32 torr 


t = 80.0 mins:

Ptot = PPH3 + PP4 + PH2

168 = 100 - 4x + x + 6x 

3x = 168 - 100

x = 22.67 torr

after 80 mins:

PPH3  = 100 - 4(17) 

PPH= 9.33 torr 


Step 3: Check if 1st order reaction: rate = k[PH3]      

  • exponent of reactant = order of reaction (if 1, not written)
  • kt=40 = kt=80


integrated rate law for a first-order reaction:


lnPt=-kt+lnP0


Solve for k at t = 40.0 mins: 


ln(32)=-k(40.0 min)+ln(100)ln(32)-ln(100)=-k(40.0 min)-1.1394-40.0 min=-k(40.0 min)-40.0 min


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Problem Details

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

4PH3(g) →P4(g) + 6H2(g) 

Time (min)        Ptotal (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(PPH3)2 

b) rate = k(PPH3)-2

c) rate = k

d) rate = k(PPH3)

e) rate = k(PPH3)-1

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