For the reaction, `X + Y to Z`, the rate is given as `k[X]^(1//3) [Y]^(1)`. Calculate the order of the reaction.

Explanation

To determine the order of the reaction for the given reaction \( X + Y \to Z \) with the rate law expression \( \text{Rate} = k[X]^{1/3}[Y]^{1} \), we can follow these steps:

### Step 1: Identify the Rate Law Expression
The rate law expression is given as:
\[ \text{Rate} = k[X]^{1/3}[Y]^{1} \]
Here, \( k \) is the rate constant, and the terms \( [X]^{1/3} \) and \( [Y]^{1} \) represent the concentrations of the reactants \( X \) and \( Y \) raised to their respective powers.

### Step 2: Determine the Powers of Concentration
From the rate law expression:
- The power of \( [X] \) is \( \frac{1}{3} \).
- The power of \( [Y] \) is \( 1 \).

### Step 3: Calculate the Total Order of the Reaction
The order of the reaction is the sum of the powers of the concentrations of the reactants in the rate law expression. Therefore, we can calculate the total order as follows:
\[ \text{Order} = \text{Power of } [X] + \text{Power of } [Y] \]
Substituting the values:
\[ \text{Order} = \frac{1}{3} + 1 \]
To add these fractions, we can convert \( 1 \) into a fraction with a common denominator:
\[ 1 = \frac{3}{3} \]
Now, we can add:
\[ \text{Order} = \frac{1}{3} + \frac{3}{3} = \frac{4}{3} \]

### Final Answer
Thus, the order of the reaction is:
\[ \text{Order} = \frac{4}{3} \]

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