Certainly! Let's work through the problem step-by-step to find the molarity of the solution and express it to two significant figures.
### Step 1: Understand the Concept of Molarity
Molarity (M) is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute divided by the volume of the solution in liters. The formula for molarity is:
[tex]\[ M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \][/tex]
### Step 2: Identify the Given Values
In this problem, we have:
- Moles of solute ([tex]\( \text{Na}_2\text{SO}_4 \)[/tex]) = 0.45 mol
- Volume of solution = 9.51 L
### Step 3: Calculate the Molarity
Using the given values, we can find the molarity as follows:
[tex]\[ \text{Molarity} = \frac{0.45 \text{ mol}}{9.51 \text{ L}} \][/tex]
[tex]\[ \text{Molarity} = 0.04731861198738171 \text{ mol/L} \][/tex]
### Step 4: Round the Molarity to Two Significant Figures
In scientific notation, it is often important to round the final answer to the appropriate number of significant figures. Given that we need to express the molarity to two significant figures:
[tex]\[ \text{Molarity rounded to two significant figures} = 0.05 \text{ mol/L} \][/tex]
### Final Answer
The molarity of the solution is [tex]\( 0.05 \)[/tex] moles per liter (mol/L) when expressed to two significant figures.
