You may have been told not to mix bleach and ammonia. The reason is that bleach (sodium hypochlorite) reacts with ammonia to produce toxic chloramines, such as NH2Cl. For example, in basic solution: OCl-1aq2 + NH31aq2S OH-1aq2 + NH2Cl1aq2 (a) The following initial rate data for this reaction were obtained in basic solution at 25 °C What is the rate law for the reaction? What is the numerical value of the rate constant k, including the correct units?

Question

You may have been told not to mix bleach and ammonia.
The reason is that bleach (sodium hypochlorite) reacts with
ammonia to produce toxic chloramines, such as NH2Cl.
For example, in basic solution:
OCl-1aq2 + NH31aq2S OH-1aq2 + NH2Cl1aq2
(a) The following initial rate data for this reaction were
obtained in basic solution at 25 °C
<TABLE>
What is the rate law for the reaction? What is the 
numerical value of the rate constant k, including the correct 
units?

Accepted Answer

Hello. In this problem we are told. The following reaction occurs in basic solution. We are given the initial rate data for the reaction at 25°C. We are asked to determine the rate law for the reaction and the numerical value for the rate constant with the correct units. Let's begin then writing the general form of the reaction rate law. So we have our right then is equal to the reaction rate constant times the concentration of hyper bro might some order X concentration of phosphate some order Y. And the concentration of hydroxide ions to some orders E. So we're including hydroxide ions because the concentration of hydroxide ions is changing in terms of ph So next step that's then find our initial concentrations of hydroxide ions. So recall that the P. O. H. Is equal to 14 minus the ph. So for the first two experiments this is 14 -10. So that's equal to four for the 3rd and 4th experiment. Then we have 14 minus 11. P. O. H. Is equal to three are hydroxide ion concentration, then is equal to 10 to the negative P. O. H. Let's tend to the -4 for the first two experiments And it's equal to 10 to the -3 for the 3rd and 4th experiment. So let's put that into our table. So we have one times 10 to the minus four for the 1st and 2nd experiment and one times 10 to minus three for the third and the fourth. Next step let's find the reaction order. Why? So the order with regard to phosphene. If we look at experiment one and two, then the ph is being held constant amount of hyper bromide is being held constant and the amount of of our false pain is changing. And so we'll compare then the rate of experiment one to that of experiment to to determine then our order. Y. So the rate of experiment to that of Experiment one, we have our reaction rate constant times the concentration of hyper bro. Might for the second reaction or experiment times concentration of phosphate. For the second experiment race to the white power times the concentration of drops indians raised the Z power. Then we do the same for our first experiment, we have the concentration of might for the first experiment raised to the X Power times the concentration of phosphorus. For the first experiment raised to the white power times concentration of hydroxide indians. For the first experiment raised to the Z power. And we see then that our reaction rate constant cancels our concentration of hypothalamic cancels, and our concentration of hydroxide ion cancels. And then we equate this to our rates. So the rate for second experiment is 0. clarity per second. And the rate for first experiment is 0.900 30 per second. Those units will cancel as well. 10 were left with 0. over 0. to the Y. This then is equal to 0.3600 over 0.0900. And so this then works out to four to the Y. is equal to four. And so therefore Y. is equal to one. So our order with regard to phosphene is one. And the next step then do similarly to find the order X. In this case we're going to prepare then experiment three and four. This is where then everything is being held constant. Except for the concentration of hyper bro. Might. So we have our reaction rate constant times the concentration of hyper bro. Might. The third experiment which is 0.150 to the X. In terms of concentration of phosphorus we now know is to the one power times the concentration of hydroxide ions, seapower all over. Then our reaction rate constant times of concentration, the type of bro might The X. Power. For the 4th experiment the concentration of phosphate. The fourth experiment times concentration of hydroxide to the Z Power. And so we get our reaction rate constants cancel. We get a concentration of phosphate to cancel. And our concentration of hydroxide cancel And then we take this and equal to the right three which is 0.0360 hilarity per second Divided by that. For the 4th experiment, 0.01 - zero hilarity per second. Are you in a similarity per second cancel This, then works out to 0.0150 divided by 0.0050 to the X. Which is equal to 0.0360 over 0. - zero. And we then get This is equal to 3 to the X. is equal to three. And so X. is also equal to one. And then step five. We're gonna find the order with regard to Z. And so we will then compare this time, experiments two and three. This is where we have the concentration of hyper bro might remain in constant concentration of phosphorus remaining constant. And only the ph is changing. So we have Great to to rate three. We have the reaction rate constant times the concentration of I have a bro might which we know is now to the one power times the concentration of phosphate which is also to the one power times the concentration of hydroxide ions to the Z power. So that's four. The second experiment for the third experiment then we have the rate constant in terms of concentration of to the one power times the concentration of phosphene to one Power times concentration drugs that island to the Z Power. It's our reaction rate constant, cancels our concentration of bromine and phosphate. And cancel. We set this equal to The rate for experiment two which is 0.3600 To that for experiment 3 : 0.0360. And we get then one times 10 to the - Number one times 10 to the minus three. Z. Power is equal to 0.3600. About two by 0.360. And so this is 1/10, Busy is equal to 10. That means guarantee Is equal to -1. So step six. Then we're now gonna write the reaction rate law with the proper orders. So we have the rate then is equal to our reaction rate constant times the concentration of hyper bro. Might for the first order times the concentration of phosphate to the first order and the concentration of hydroxide ions the minus one. And so we can rewrite this and put the hydroxide iron in the denominator. The rate is equal to the reaction rate constant times the concentration of hippodrome. Might for the first hour Power times the concentration of phosphene. The first order all over the concentration of hydroxide brian. And then the last thing we need to do is to solve for K. Using um The first experiment. So we'll take our reaction rate law and we'll rearrange it to isolate K. So we move everything else to the left hand side. So we get K. Then is equal to great time to hydroxide ion concentration divided by the hipaa bromide ion concentration divided by concentration. And this works out to them. The rate for the first experiment is 0. Liberty per second are hydroxide in concentration is one Times 10 to the - Mueller. Are hipAA broke. My concentration is 0.150 Mueller. And our phosphate concentration is 0. Mueller. And so then looking at our units so we have similarity Squared um in the numerator and hilarity squared in the denominator. So that cancels and we're left with just per seconds. So our reaction rate constant K. Then is going to be equal to 0.12 seconds to the -1. So we found that our reaction rate constant. Okay as an American value of 0.12 and the units are per second and the reaction rate law then his first order with regard to Hipaa bro. Might first order with regard to phosphene and minus one order with regard to hydroxide. Thanks for watching. Hope this help

Verified Solution

Key Concepts

Rate Law

Rate Constant (k)

Reaction Order