Chemical Kinetics Question

[deleted647690]

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For the hypothetical reaction listed below, the rate of disappearance of A is 0.450 M/sec:

2A--->B+C

The rate of appearnce of B is which of the following?
A. 0.225
B. .450
C. .900
D. -0.450


Would it be A? Since rate of change of A/time = rate of change of B/time *2

But why would it not be negative?

 

[pioneer22]

Yes, A.

It is positive since the rate of appearance of products is always positive, while rate of appearance of reactants is negative.

 

[aldol16]

Sign conventions are only useful for systems with established coordinates. For instance, if I said Jim pushed Tom 3 meters in the +x direction and then Sam pushed Tom 4 meters in the -x direction, you could easily convey that by saying +3 + (-4). The sign is useful here because it allows you to denote directionality. In other words, you can just say that Jim pushed Tom +3 m and Sam pushed Tom -4 m, where the coordinate system you define is positive in the direction of the initial push. But if I then tell you that +x is due east and -x is due west and then ask you how Sam pushed Tom, you could just as easily say 4 m due west, as opposed to -4 m. In fact, the former is probably even clearer than the latter in that case.

Same scenario here. If I'm asking for a rate of appearance of something, I've already established "directionality." The pure form is -1/2*dA/dt = dB/dt. In other words, the disappearance of A (the negative sign conveys disappearance) is related to the appearance of B in that equation by the constant 1/2. If I ask you the rate of change of B, then it would be appropriate for you to include sign. But it's asking the rate of appearance of B, which already defines the sign for you.