What volume, in liters, of 2.0 M NaOH solution can be made using 500.0 g NaOH?
[tex]$NaOH : 39.997 g / mol$[/tex]
[?] L
Answer (2)
The volume of a 2.0 M NaOH solution that can be made from 500.0 g of NaOH is approximately 6.25 liters. This is calculated by finding the number of moles of NaOH and then using the molarity formula to determine the volume. Therefore, you can create 6.25 L of the solution.
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Calculate the number of moles of N a O H : m o l es = 39.997 g/mol 500.0 g = 12.50 mol .
Use the molarity formula to find the volume: V o l u m e = M o l a r i t y m o l es .
Substitute the values: V o l u m e = 2.0 M 12.50 mol = 6.25 L .
The volume of 2.0 M N a O H solution is 6.25 L .
Explanation
Problem Analysis We are given the mass of N a O H (500.0 g), the molar mass of N a O H (39.997 g/mol), and the desired molarity of the N a O H solution (2.0 M). We need to find the volume of the N a O H solution in liters.
Calculating Moles of NaOH First, we need to calculate the number of moles of N a O H using the formula: m o l es = m o l a r _ ma ss ma ss Substituting the given values: m o l es = 39.997 g/mol 500.0 g = 12.500937570317774 mol Rounding to a reasonable number of significant figures, we get approximately 12.50 mol.
Calculating Volume of NaOH Solution Next, we use the definition of molarity to find the volume of the solution. Molarity is defined as: M o l a r i t y = V o l u m e ( in L ) m o l es We can rearrange this formula to solve for volume: V o l u m e ( in L ) = M o l a r i t y m o l es Substituting the calculated number of moles and the given molarity: V o l u m e ( in L ) = 2.0 M 12.500937570317774 mol = 6.250468785158887 L Rounding to a reasonable number of significant figures, we get approximately 6.25 L.
Final Answer Therefore, the volume of 2.0 M N a O H solution that can be made using 500.0 g N a O H is approximately 6.25 L.
Examples
In a lab setting, you might need to prepare a specific concentration of a solution for an experiment. For example, if you need a 2.0 M NaOH solution for a titration, you would use the calculation above to determine how much NaOH to dissolve in a certain volume of water. This ensures that your experiment has the correct concentration of reactants, leading to accurate results. Understanding molarity and solution preparation is crucial in many scientific fields, including chemistry, biology, and medicine.
