100 mL of Na$_3$PO$_4$ solution contains 3.45 g of sodium. The molarity of the solution is __________ $\times$10$^{-2}$ mol L$^{-1}$. (Nearest integer) [Atomic Masses - Na: 23.0 u, O: 16.0 u, P: 31.0 u]

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Step 1: Understanding the Question We are given the volume of a sodium phosphate (Na$_3$PO$_4$) solution and the mass of sodium ions it contains. We need to calculate the molarity of the Na$_3$PO$_4$ solution. Step 2: Key Formula or Approach Molarity (M) is defined as the number of moles of solute per liter of solution. $$ \text{Molarity} = \frac{\text{Moles of solute}}{\text{Volume of solution in L}} $$ We can find the moles of Na$_3$PO$_4$ from the given mass of sodium. Step 3: Detailed Calculation Calculate moles of Sodium (Na): Given mass of Na = 3.45 g Atomic mass of Na = 23.0 g/mol $$ \text{Moles of Na} = \frac{\text{Mass}}{\text{Atomic mass}} = \frac{3.45 \text{ g}}{23.0 \text{ g/mol}} = 0.15 \text{ mol} $$ Calculate moles of Sodium Phosphate (Na$_3$PO$_4$): From the chemical formula Na$_3$PO$_4$, we can see that 1 mole of Na$_3$PO$_4$ contains 3 moles of Na atoms. $$ \text{Moles of Na}_3\text{PO}_4 = \frac{\text{Moles of Na}}{3} = \frac{0.15 \text{ mol}}{3} = 0.05 \text{ mol} $$ Calculate Molarity: Moles of solute (Na$_3$PO$_4$) = 0.05 mol Volume of solution = 100 mL = 0.100 L $$ \text{Molarity} = \frac{0.05 \text{ mol}}{0.100 \text{ L}} = 0.5 \text{ mol L}^{-1} $$ Express the answer in the required format: The question asks for the answer in the format of _________ $\times$ 10$^{-2}$ mol L$^{-1}$. $$ 0.5 = 50 \times 10^{-2} $$ Step 4: Final Answer The molarity is 0.5 M, which is equal to 50 $\times$ 10$^{-2}$ M. The nearest integer value is 50.

100 mL of Na\(_3\)PO\(_4\) solution contains 3.45 g of sodium. The molarity of the solution is __________ \(\times\)10\(^{-2}\) mol L\(^{-1}\). (Nearest integer)
[Atomic Masses - Na: 23.0 u, O: 16.0 u, P: 31.0 u]

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Correct Answer: 50

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100 mL of Na\(_3\)PO\(_4\) solution contains 3.45 g of sodium. The molarity of the solution is __________ \(\times\)10\(^{-2}\) mol L\(^{-1}\). (Nearest integer) [Atomic Masses - Na: 23.0 u, O: 16.0 u, P: 31.0 u]