Question

given the balanced chemical equation for the decomposition of ino, and the rate of disappearance of ino, complete the expressions for the rates of appearance of \\(\text{i}_2\\) and \\(\text{no}\\).

\\2\text{ino}(g) \longrightarrow \text{i}_2(g) + 2\text{no}(g)\\

do not include spaces anywhere in your answer.

\\(-\frac{\delta\text{ino}}{2\delta t} = \frac{\delta\quad}{\delta\quad} = \frac{\delta\quad}{2\delta\quad}\\)

Explanation:

Identify the balanced chemical equation

The given balanced chemical equation is:

$$2\text{INO}(g) \longrightarrow \text{I}_2(g) + 2\text{NO}(g)$$

Relate the rates of consumption and formation

For a general reaction \(a\text{A} \longrightarrow b\text{B} + c\text{C}\), the unique rate of reaction is related to the individual rates of change in concentration by:

$$\text{Rate} = -\frac{1}{a}\frac{\Delta[\text{A}]}{\Delta t} = \frac{1}{b}\frac{\Delta[\text{B}]}{\Delta t} = \frac{1}{c}\frac{\Delta[\text{C}]}{\Delta t}$$

Applying this to our reaction:

$$-\frac{\Delta[\text{INO}]}{2\Delta t} = \frac{\Delta[\text{I}_2]}{\Delta t} = \frac{\Delta[\text{NO}]}{2\Delta t}$$

Express the rate of disappearance of INO

The rate of disappearance of \(\text{INO}\) is expressed as a positive quantity:

$$-\frac{\Delta[\text{INO}]}{\Delta t}$$

The problem provides the starting term as:

$$-\frac{\Delta[\text{INO}]}{2\Delta t}$$

Determine the first blank expression

We equate the starting term to the rate of appearance of \(\text{I}_2\):

$$-\frac{\Delta[\text{INO}]}{2\Delta t} = \frac{\Delta[\text{I}_2]}{\Delta t}$$

Looking at the input fields, the first blank is a fraction:

$$\frac{\Delta[\text{I}_2]}{\Delta t}$$

In the image, the template for the first blank has a \(\Delta\) in the numerator and a \(\Delta\) in the denominator:
Numerator: \(\Delta [\text{I}_2]\)
Denominator: \(\Delta t\)

Determine the second blank expression

We equate the starting term to the rate of appearance of \(\text{NO}\):

$$-\frac{\Delta[\text{INO}]}{2\Delta t} = \frac{\Delta[\text{NO}]}{2\Delta t}$$

Looking at the template for the second blank, the denominator is already given as \(2\Delta t\).
The numerator template has a \(\Delta\) followed by a box:
Numerator: \(\Delta [\text{NO}]\)

Answer:

Given the balanced chemical equation for the decomposition of INO, and the rate of disappearance of INO, complete the expressions for the rates of appearance of \(\text{I}_2\) and \(\text{NO}\).

$$2\text{INO}(g) \longrightarrow \text{I}_2(g) + 2\text{NO}(g)$$

$$-\frac{\Delta[\text{INO}]}{2\Delta t} = \frac{\Delta\text{[I}_2\text{]}}{\Delta\text{t}} = \frac{\Delta\text{[NO]}}{2\Delta\text{t}}$$