A student has a 1 g sample of each of the following compounds: [tex][tex]$NaCl$[/tex][/tex], [tex]$KBr$[/tex], and [tex]$KCl$[/tex]. Which of the following lists the samples in order of increasing number of moles in the sample?

A. [tex]$NaCl \ \textless \ KCl \ \textless \ KBr$[/tex]
B. [tex][tex]$NaCl \ \textless \ KBr \ \textless \ KCl$[/tex][/tex]
C. [tex]$KCl \ \textless \ NaCl \ \textless \ KBr$[/tex]
D. [tex]$KBr \ \textless \ KCl \ \textless \ NaCl$[/tex]



Answer :

To solve this question, let's first understand the concepts involved:

### Step-by-Step Solution:

1. Molar Mass Calculation:
The molar masses of the compounds involved are:
- Sodium chloride ([tex]$NaCl$[/tex]) = 58.44 g/mol
- Potassium chloride ([tex]$KCl$[/tex]) = 74.55 g/mol
- Potassium bromide ([tex]$KBr$[/tex]) = 119.00 g/mol

2. Calculating Moles:
The number of moles in a given sample can be calculated using the formula:
[tex]\[ \text{Number of moles} = \frac{\text{Mass in grams}}{\text{Molar mass in g/mol}} \][/tex]

Given that the mass of each sample is 1 gram, we calculate the number of moles for each compound:

- For [tex]$NaCl$[/tex]:
[tex]\[ \text{Moles of } NaCl = \frac{1 \text{ g}}{58.44 \text{ g/mol}} = 0.01711 \text{ moles} \approx 0.017 \][/tex]

- For [tex]$KCl$[/tex]:
[tex]\[ \text{Moles of } KCl = \frac{1 \text{ g}}{74.55 \text{ g/mol}} = 0.01341 \text{ moles} \approx 0.013 \][/tex]

- For [tex]$KBr$[/tex]:
[tex]\[ \text{Moles of } KBr = \frac{1 \text{ g}}{119.00 \text{ g/mol}} = 0.00840 \text{ moles} \approx 0.008 \][/tex]

3. Ordering by Increasing Number of Moles:

We now need to arrange these values in increasing order. The calculated moles in ascending order are:
[tex]\[ 0.008 \text{ moles (KBr)} < 0.013 \text{ moles (KCl)} < 0.017 \text{ moles (NaCl)} \][/tex]

In terms of the compounds, it translates to:
[tex]\[ KBr < KCl < NaCl \][/tex]

4. Conclusion:
Therefore, the correct order of increasing number of moles is:

[tex]\( \boxed{KBr < KCl < NaCl} \)[/tex]

The choice that matches this order in the given question is:
[tex]\[ (D) KBr < KCl < NaCl \][/tex]