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Consider the reactions
$$X + 2Y \rightarrow 3Z\\2X + Z \rightarrow Y.$$
Let $n_{X}$, $n_{Y}$, $n_{Z}$ denote the numbers of molecules of chemicals $X, Y, Z$ in the reaction chamber. Then which of the following is conserved by both reactions?

  1. $n_{X} + n_{Y} + n_{Z}$.
  2. $n_{X}+ 7n_{Y} + 5n_{Z}$.
  3. $2n_{X} + 9n_{Y} − 3n_{Z}$.
  4. $3n_{X} − 3n_{Y} + 13n_{Z}$.
  5. None of the above.
asked in Linear Algebra by Veteran (39.7k points) 256 1308 1941 | 195 views

1 Answer

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Bassicaly here we need to find the number of molecules are same before and after the reaction ie. the conservation of mass.

To check that just take options and eliminate one by one.Following is the breakdown of options

In first reaction put the values of option a) n+2n = 3n ie. true for second equation if we put the values we get 2n+n = n so option a) is conserving mass for equation 1 but not for equation 2.

similarly elimnating all options we can conclude option b) is correct. As for equation 1  n + 2*7n = 3*5n, for equation 2  2n + 5n =7n so mass is conserved for both reactions.
answered by (11 points) 1

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