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]
