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Chemistry-

General

Easy

Question

For the chemical reaction $A plus B plus C rightwards arrow E$ , the rate of the reaction is doubled when the concentration of B was doubled, and when the concentration, of both A and B was doubled rate become doubled and when the concentration of both B and C was doubled rate become quadrupled. What is the order with respect to A, B, and C and the total order?

0, 1, 2; 3
1, 1, 0; 2
0, 1, 1; 2
1, 0, 2; 3

The correct answer is: 1, 1, 0; 2

Let the rate of the reaction is
$r equals k open square brackets A close square brackets to the power of x end exponent open square brackets B close square brackets to the power of y end exponent$
$r subscript 1 end subscript equals 3.0 cross times 10 to the power of negative 3 end exponent equals k open square brackets 0.25 close square brackets to the power of x end exponent open square brackets 0.25 close square brackets to the power of y end exponent$ …(i)
$r subscript 2 end subscript equals 6.0 cross times 10 to the power of negative 3 end exponent equals k open square brackets 0.5 close square brackets to the power of x end exponent open square brackets 0.25 close square brackets to the power of y end exponent$ …(ii)
$r subscript 3 end subscript equals 1.20 cross times 10 to the power of negative 2 end exponent equals k open square brackets 0.5 close square brackets to the power of x end exponent open square brackets 0.5 close square brackets to the power of y end exponent$ …(iii)
Divide equation (ii) by (i)
$fraction numerator 6.0 cross times 10 to the power of negative 3 end exponent over denominator 3.0 cross times 10 to the power of negative 3 end exponent end fraction equals fraction numerator k open square brackets 0.5 close square brackets to the power of x end exponent open square brackets 0.25 close square brackets to the power of y end exponent over denominator k open square brackets 0.25 close square brackets to the power of x end exponent open square brackets 0.25 close square brackets to the power of y end exponent end fraction$
$open parentheses 2 close parentheses to the power of 1 end exponent equals open parentheses 2 close parentheses to the power of x end exponent rightwards double arrow x equals 1$
Divide equation (iii) by (ii)
$fraction numerator 1.20 cross times 10 to the power of negative 2 end exponent over denominator 6.0 cross times 10 to the power of negative 3 end exponent end fraction equals fraction numerator k open square brackets 0.5 close square brackets to the power of x end exponent open square brackets 0.5 close square brackets to the power of y end exponent over denominator k open square brackets 0.5 close square brackets to the power of x end exponent open square brackets 0.25 close square brackets to the power of y end exponent end fraction$
$therefore open parentheses 2 close parentheses to the power of 1 end exponent equals open parentheses 2 close parentheses to the power of y end exponent rightwards double arrow y equals 1$
$therefore r equals k open square brackets A close square brackets to the power of 1 end exponent open square brackets B close square brackets to the power of 1 end exponent$
Total order $equals 1 plus 1 equals 2$

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