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


89% (381 ratings)
View Complete Written Solution
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

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Rate Law concept. You can view video lessons to learn Rate Law. Or if you need more Rate Law practice, you can also practice Rate Law practice problems.