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Chapter 2: Problem 116

How many grams of \(\mathrm{NaOH}\) are in \(500 \mathrm{~mL}\) of a \(0.50 \mathrm{M}\) solution?

Short Answer

Expert verified
There are 10 grams of NaOH in the solution.

Step by step solution

01

Understanding Molarity

Molarity ( ext{M}) is defined as the number of moles of solute per liter of solution. The formula to calculate molarity is: \[ ext{Molarity} = rac{ ext{Moles of solute}}{ ext{Volume of solution in liters}} \]Here, we have a 0.50 M NaOH solution, and we need this information to find the moles of NaOH.
02

Converting Volume to Liters

The volume of the solution is given in milliliters, and we need to convert it into liters since molarity is moles per liter. \[ 500 ext{ mL} = 0.500 ext{ L} \] Now, use this volume for the calculation of moles of NaOH.
03

Calculating Moles of NaOH

Using the molarity formula, we can calculate the moles of NaOH:\[ ext{Moles of NaOH} = ext{Molarity} imes ext{Volume in liters} = 0.50 imes 0.500 = 0.25 ext{ moles} \] This tells us the number of moles of NaOH in the solution.
04

Finding Molar Mass of NaOH

The molar mass of NaOH is calculated by adding the atomic masses of sodium (Na), oxygen (O), and hydrogen (H):\[ ext{Molar mass of NaOH} = 22.99 ( ext{Na}) + 16.00 ( ext{O}) + 1.01 ( ext{H}) = 40.00 ext{ g/mol} \]
05

Calculating Grams of NaOH

Now that we know the moles of NaOH and its molar mass, we can find the mass in grams:\[ ext{Mass in grams} = ext{moles} imes ext{molar mass} = 0.25 imes 40.00 = 10.00 ext{ grams} \]
06

Final Answer

Thus, there are 10 grams of NaOH in the 500 mL of a 0.50 M solution.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Moles of Solute
The concept of moles is central to chemistry and a key to understanding molarity calculations. A mole is a measure for the amount of substance, similar to how a dozen measures quantity, but instead, a mole is much larger. It represents Avogadro's number, which is approximately \(6.022 \times 10^{23}\) entities (atoms, molecules, etc.).
The moles of solute in a solution can be calculated using the molarity formula:
  • Molarity \( = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}}\)
This formula can be rearranged to find the moles of the solute if you know the molarity and the volume of the solution:
  • Moles of solute \( = \text{Molarity} \times \text{Volume in liters}\)
In the case of our problem, we have a 0.50 M solution, and by converting that to moles using a volume of 0.500 L, we find there are 0.25 moles of NaOH.
Molar Mass Calculation
To convert moles of a substance to grams, you need to know the substance's molar mass. Molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol).
To calculate the molar mass of a compound like NaOH, you add the atomic masses of its constituent elements:
  • Sodium (Na) has an atomic mass of 22.99 g/mol.
  • Oxygen (O) has an atomic mass of 16.00 g/mol.
  • Hydrogen (H) has an atomic mass of 1.01 g/mol.
Adding these together gives the molar mass of NaOH:
  • Molar mass of NaOH = 22.99 + 16.00 + 1.01 = 40.00 g/mol
Once you have the molar mass, you can find the mass in grams by multiplying the moles of the solute by the molar mass:
  • Grams of NaOH = 0.25 moles \(\times\) 40.00 g/mol = 10 grams
Volume Conversion to Liters
When dealing with molarity calculations, it's essential to express volume in liters because molarity is defined as moles per liter. Often, problems will present the volume in milliliters, requiring conversion to liters.To convert milliliters to liters, you use the conversion factor \(1 \text{ liter} = 1000 \text{ milliliters}\). This means you divide the number of milliliters by 1000:
  • Volume in liters = Volume in milliliters / 1000
For example, converting 500 milliliters to liters would be:
  • 500 mL = \(\frac{500}{1000}\) L = 0.500 L
This simple but crucial step ensures you can accurately use the molarity formula to find the moles of solute.

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Most popular questions from this chapter

Calculate the volume of \(0.25 \mathrm{M}\) NaI that would be needed to react with all of the \(\mathrm{Hg}^{2+}\) ion from \(45 \mathrm{~mL}\) of $$ \begin{array}{l} \text { a } 0.10 \mathrm{M} \mathrm{Hg}\left(\mathrm{NO}_{3}\right)_{2} \text { solution. } \\ \qquad \begin{array}{l} 2 \mathrm{Nal}(a q)+\mathrm{Hg}\left(\mathrm{NO}_{3}\right)_{2}(a q) \\ \longrightarrow \mathrm{HgI}_{2}(s)+2 \mathrm{NaNO}_{3}(a q) \end{array} \end{array} $$

How many moles of \(\mathrm{CO}_{2}\) are produced when 5 moles of \(\mathrm{O}_{2}\) are consumed in the following reaction? $$ 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g) $$

How many moles of \(\mathrm{CuO}\) would be required to produce 12 mol of copper metal in the following reaction? $$ \mathrm{CuO}(s)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{Cu}(s)+\mathrm{H}_{2} \mathrm{O}(g) $$

Assume that two experiments are performed on the following chemical reaction: $$ \begin{array}{lccl} 2 \mathrm{Br}^{-}(a q) & \+ & \mathrm{Cl}_{2}(a q) & \longrightarrow & \mathrm{Br}_{2}(a q)+ & 2 \mathrm{Cl}^{-}(a q) \\ \text { Colorless } & \text { Colorless } & \text { Red } & \text { Colorless } \end{array} $$ \- Experiment \(1: 100 \mathrm{~mL}\) of a \(0.0100 \mathrm{M}\) solution of \(\mathrm{Br}^{-}\) are added to \(100 \mathrm{~mL}\) of a \(0.0200 \mathrm{M}\) solution of \(\mathrm{Cl}_{2}\) \- Experiment \(2: 100 \mathrm{~mL}\) of a \(0.0100 \mathrm{M}\) solution of \(\mathrm{Br}^{-}\) are added to \(100 \mathrm{~mL}\) of a \(0.0500 \mathrm{M}\) solution of \(\mathrm{Cl}_{2}\) If the reaction between aqueous solutions of the \(\mathrm{Br}^{-}\) ion and \(\mathrm{Cl}_{2}\) goes to completion, which of the following would you expect to observe after mixing the two solutions? Explain your answer. (a) The solution formed in experiment 1 will be a darker red. (b) The solution formed in experiment 2 will be a darker red. (c) The solutions formed in both experiments will be the same shade of red.

How many hydrogen atoms are present in \(1.00 \mathrm{~mol}\) of hydrogen gas, \(\mathrm{H}_{2}\) ? How many \(\mathrm{H}_{2}\) molecules? What is the mass of the sample?
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