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Chapter 12: Problem 201

How many grams of \(\mathrm{NaOH}\) are needed to prepare \(500.0 \mathrm{~mL}\) of \(0.300 \mathrm{M} \mathrm{NaOH}\) solution?

Short Answer

Expert verified
To prepare 500.0 mL of 0.300 M NaOH solution, 6.0 g of NaOH are needed.

Step by step solution

01

Understand the Problem and Gather Information

The problem is essentially asking to find out how many grams of NaOH are needed to prepare a 0.300 M solution of NaOH in a volume of 500.0 mL. The molar mass of NaOH is calculated by adding the atomic masses of sodium (Na - 23 g/mol), oxygen (O - 16 g/mol), and hydrogen (H - 1 g/mol), which results in 40 g/mol.
02

Convert Volume from mL to L

Since molarity is defined in terms of liters of solution, the given volume (500 ml) has to be converted to liters. This is done using the conversion factor of 1 L = 1000 ml, resulting in: \[ 500.0 mL * \frac{1 L}{1000 mL} = 0.5 L \]
03

Use the Molarity Formula to Find Moles of NaOH

Using the formula of molarity from earlier: \[Molarity = \frac{Moles~of~Solute}{Liters~of~Solution}\] the moles of NaOH can be found by rearranging the formula as follows: \[Moles~of~Solute = Molarity * Liters~of~Solution\] Then substituting the given molarity (0.300 M) and the converted volume (0.5 L): \[Moles~of~NaOH = 0.300 M * 0.5 L = 0.15 mol\]
04

Convert Moles to Grams using Molar Mass

The final step involves converting the moles of NaOH to grams. This is done by multiplying the moles of NaOH by the molar mass of NaOH (40 g/mol): \[Grams~of~NaOH = Moles~of~NaOH * Molar~Mass~of~NaOH = 0.15 mol * 40 g/mol = 6.0 g\] In conclusion, 6.0 g of NaOH are needed to prepare 500.0 mL of a 0.300 M NaOH solution.

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Most popular questions from this chapter

When \(5.00 \mathrm{~g}\) of a solute is dissolved in sufficient solvent to produce \(100.0 \mathrm{~mL}\) of solution, (a) What is the percent by mass/volume concentration of the solute? (b) What additional information do you need to calculate the percent by mass concentration of the solute, and how would you calculate that concentration once you had the missing information?

Calculate the molarity of pure water at \(4.0^{\circ} \mathrm{C}\). The density of water at \(4.0^{\circ} \mathrm{C}\) is \(1.0000 \mathrm{~g} / \mathrm{mL}\).

A \(50.00\) -mL sample of hydrochloric acid of unknown concentration was neutralized by \(47.35 \mathrm{~mL}\) of \(0.01020 \mathrm{M}\) sodium hydroxide solution. Calculate the concentration of the original HCl solution.

What is the mass in grams of the nitrogen atoms in \(100.0 \mathrm{~mL}\) of \(1.00 \mathrm{M} \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\) solution?

(a) Use these data to plot solubility as a function of temperature for \(\mathrm{KCl}\) and \(\mathrm{Li}_{2} \mathrm{SO}_{4}:\) (b) Using the plot, estimate the solubility of both compounds in water at \(70^{\circ} \mathrm{C}\). (c) How much of each compound can be dissolved in a beaker containing \(75 \mathrm{~g}\) of water at \(70^{\circ} \mathrm{C} ?\)
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