Which solution is the most concentrated?

A. [tex]$2.0 \text{ mL}$[/tex] of [tex]$10 \text{ M } H_2SO_4$[/tex], where [tex]$H_2SO_4$[/tex] has a molar mass of [tex]$98 \text{ g/mol}$[/tex]

B. [tex]$5.0 \text{ mL}$[/tex] of [tex]$1.0 \text{ M } PbSO_4$[/tex], where [tex]$PbSO_4$[/tex] has a molar mass of [tex]$303 \text{ g/mol}$[/tex]

C. [tex]$2.0 \text{ mL}$[/tex] of [tex]$10.5 \text{ M } H_2O_2$[/tex], where [tex]$H_2O_2$[/tex] has a molar mass of [tex]$34 \text{ g/mol}$[/tex]

D. [tex]$100 \text{ mL}$[/tex] of [tex]$10 \text{ M } NaCl$[/tex], where [tex]$NaCl$[/tex] has a molar mass of [tex]$58 \text{ g/mol}$[/tex]



Answer :

To determine which solution is the most concentrated, we compare the concentrations given in molarity (M), which is a measure of the number of moles of solute per liter of solution.

Let's list the concentrations provided for each solution:

1. [tex]\(2.0 \text{ mL}\)[/tex] of [tex]\(10 \text{ M} \, \text{H}_2\text{SO}_4\)[/tex]
2. [tex]\(5.0 \text{ mL}\)[/tex] of [tex]\(1.0 \text{ M} \, \text{PbSO}_4\)[/tex]
3. [tex]\(2.0 \text{ mL}\)[/tex] of [tex]\(10.5 \text{ M} \, \text{H}_2\text{O}_2\)[/tex]
4. [tex]\(100 \text{ mL}\)[/tex] of [tex]\(10 \text{ M} \, \text{NaCl}\)[/tex]

Since the molarities of the solutions are already provided, we will directly compare these values:

1. [tex]\( \text{H}_2\text{SO}_4 \)[/tex] has a concentration of [tex]\(10 \text{ M}\)[/tex].
2. [tex]\( \text{PbSO}_4 \)[/tex] has a concentration of [tex]\(1.0 \text{ M}\)[/tex].
3. [tex]\( \text{H}_2\text{O}_2 \)[/tex] has a concentration of [tex]\(10.5 \text{ M}\)[/tex].
4. [tex]\( \text{NaCl} \)[/tex] has a concentration of [tex]\(10 \text{ M}\)[/tex].

The most concentrated solution is the one with the highest molarity. Comparing the given concentrations, we have:
- [tex]\(10 \text{ M}\)[/tex] for [tex]\( \text{H}_2\text{SO}_4 \)[/tex]
- [tex]\(1.0 \text{ M}\)[/tex] for [tex]\( \text{PbSO}_4 \)[/tex]
- [tex]\(10.5 \text{ M}\)[/tex] for [tex]\( \text{H}_2\text{O}_2 \)[/tex]
- [tex]\(10 \text{ M}\)[/tex] for [tex]\( \text{NaCl} \)[/tex]

The highest molarity among these values is [tex]\(10.5 \text{ M}\)[/tex]. Therefore, the most concentrated solution is:

[tex]\(2.0 \text{ mL}\)[/tex] of [tex]\(10.5 \text{ M} \, \text{H}_2\text{O}_2\)[/tex].