Question

select the correct answer.
in this equation, what should be the coefficients of the reactants and products?
( i_{2}+o_{2}
ightarrow i_{4}o_{9} )
a. the coefficient of iodine is 2, oxygen is 9, and the product is 2
b. the coefficient of iodine is 9, oxygen is 4, and the product is 2
c. the coefficient of iodine is 4, oxygen is 9, and the product is 2
d. the coefficient of iodine is 2, oxygen is 9, and the product is 1

Explanation:

Step1: Balance the iodine atoms

The chemical formula of the product is \(I_4O_9\). For the iodine atoms, if we assume the coefficient of \(I_2\) is \(x\) and the coefficient of \(I_4O_9\) is \(y\), from the conservation of iodine atoms \(2x = 4y\). Let \(y = 2\), then \(x=4\). But this is wrong. Let's start from the oxygen atoms.

Step2: Balance the oxygen atoms

Let the coefficient of \(O_2\) be \(a\) and the coefficient of \(I_4O_9\) be \(b\). From the conservation of oxygen atoms \(2a=9b\). Let \(b = 2\), then \(a = 9\).

Step3: Balance the iodine atoms again

Now, for iodine atoms, in \(I_2\) and \(I_4O_9\). Let the coefficient of \(I_2\) be \(c\). Since in \(I_4O_9\) (coefficient \(b = 2\)) there are \(4\times2 = 8\) iodine atoms. If the coefficient of \(I_2\) is \(c\), then \(2c=8\), \(c = 4\). But wait, let's write the balanced equation: \(4I_2+9O_2 = 2I_4O_9\)

Answer:

A. the coefficient of iodine is 2, oxygen is 9, and the product is 2 (This option is wrong. The correct balanced equation is \(4I_2 + 9O_2=2I_4O_9\), so there is no correct option in the given choices. But if we assume there is a typo and in the formula of reactant \(I_2\) is considered as \(I\) (which is wrong in chemical formula, but if we force - match):
Let's use another way. Let the balanced equation be \(aI_2 + bO_2=cI_4O_9\).
From \(I\): \(2a = 4c\); from \(O\): \(2b=9c\). Let \(c = 2\), then \(a = 4\), \(b = 9\). But if we assume the problem has a mis - written formula (maybe \(I\) instead of \(I_2\) for reactant iodine), for \(aI + bO_2=cI_4O_9\), from \(I\): \(a = 4c\), from \(O\): \(2b=9c\). If \(c = 2\), \(a = 8\), \(b = 9\) (still wrong). If we consider the closest match in the given options (assuming some error in problem - making), maybe the intended answer is A (but strictly chemically, the options are wrong. If we assume the formula of reactant iodine is \(I\) (non - existent in nature, \(I_2\) is the diatomic form), for \(2I+9O_2 = 2I_4O_9\) (iodine balance: left \(2\), right \(8\) (wrong); oxygen balance: left \(18\), right \(18\)) )