Mass of Solute in a Solution of Known Molarity Presentation

Solution concentration

Mass of Solute in a Solution of Known Molarity

A known molarity tells how many moles of solute are dissolved in each liter of solution. From there, molar mass converts moles into grams.

\(n = M \times V\), then \(m = n \times M_{\mathrm{molar}}\)

Learning target: calculate solute mass from molarity, solution volume, and molar mass.

Given

Molarity and volume

Use concentration and solution volume to find moles of solute.

Convert

Moles to grams

Use molar mass from the chemical formula.

Result

Mass of solute

The answer tells how many grams must be dissolved in the solution.

Why it matters

Molarity lets chemists prepare solutions accurately

If a recipe says to prepare \(500.0\ \mathrm{mL}\) of \(0.250\ \mathrm{M}\) NaCl, the molarity and volume determine the number of moles of NaCl needed.

NaCl(s) → Na⁺(aq) + Cl⁻(aq)

After finding the moles, the molar mass of NaCl converts the amount into a measurable mass in grams.

This skill is used to prepare

salt solutions such as NaCl(aq),
ionic solutions such as CaCl₂(aq),
transition-metal solutions such as CuSO₄(aq),
standards for titrations and calibrations,
reaction mixtures with controlled concentration.

Core concept

Concentration tells moles per liter

Molarity is the ratio of moles of solute to liters of solution:

\[ M = \frac{n}{V} \] \[ n = M \times V \]

The volume must be in liters when using \(n = M \times V\). For example, \(250.0\ \mathrm{mL} = 0.2500\ \mathrm{L}\).

Vocabulary

Variables and units in solute-mass calculations

Quantity	Meaning	Formula or source	Unit
Molarity, \(M\)	Concentration of solute in solution	\(M = \frac{n}{V}\)	mol/L or M
Moles, \(n\)	Amount of solute	\(n = M \times V\)	mol
Volume, \(V\)	Total solution volume	Convert mL to L	L
Molar mass, \(M_{\mathrm{molar}}\)	Mass of \(1\ \mathrm{mol}\) of solute	Periodic table and formula	g/mol
Mass, \(m\)	Mass of solute needed	\(m = n \times M_{\mathrm{molar}}\)	g

Important: \(500.0\ \mathrm{mL}\) must become \(0.5000\ \mathrm{L}\) before using \(n = M \times V\).

Main relationship

Use a two-step calculation path

Known molarity and volume give moles. Molar mass converts those moles into grams.

Known molarity \(M\), in mol/L

Known volume convert mL to L

Moles of solute \(n = M \times V\)

Mass of solute \(m = n \times M_{\mathrm{molar}}\)

\[ m = M \times V_{\mathrm{L}} \times M_{\mathrm{molar}} \]

This combined equation works only when \(V\) is in liters and molar mass is in \(\mathrm{g/mol}\).

Interactive simulation

Calculate solute mass from molarity and volume

Choose solute and solution size

0.250 M NaCl × 0.5000 L × 58.44 g/mol = 7.31 g NaCl

Molarity 0.250 M

Solution volume 500.0 mL

Calculated result

Volume in liters 0.5000 L

Moles of solute 0.125 mol

Molar mass 58.44 g/mol

Mass of solute 7.31 g

Dissolve 7.31 g NaCl and add water until the total solution volume is 500.0 mL.

Static fallback: \(0.250\ \mathrm{M}\) NaCl and \(500.0\ \mathrm{mL}\) require \(7.31\ \mathrm{g}\) NaCl.

Dynamic relationship

Mass increases with molarity, volume, and molar mass

The bars show how the calculation builds from concentration and volume to moles, then from moles to grams.

Interpretation: doubling the volume at the same molarity doubles the moles of solute, so the required mass also doubles.

Worked example

Find the mass of NaCl needed

Problem: What mass of NaCl is needed to prepare \(500.0\ \mathrm{mL}\) of \(0.250\ \mathrm{M}\) NaCl?

1. Convert volume to liters. \[ 500.0\ \mathrm{mL} = 0.5000\ \mathrm{L} \]
2. Use molarity to find moles of solute. \[ n_{\mathrm{NaCl}} = M \times V = 0.250\ \mathrm{mol/L} \times 0.5000\ \mathrm{L} = 0.125\ \mathrm{mol} \]
3. Convert moles to grams using molar mass. \[ m_{\mathrm{NaCl}} = 0.125\ \mathrm{mol} \times 58.44\ \mathrm{g/mol} = 7.31\ \mathrm{g} \]
Final answer: Dissolve \(7.31\ \mathrm{g}\) NaCl, then add water until the final solution volume is \(500.0\ \mathrm{mL}\).

Common mistake

Do not multiply molarity by milliliters

Incorrect

A student calculates \(0.250\ \mathrm{M} \times 500.0\ \mathrm{mL} = 125\ \mathrm{mol}\).

This is not reasonable because molarity means \(\mathrm{mol/L}\), not \(\mathrm{mol/mL}\).

Correct

Convert \(500.0\ \mathrm{mL}\) to \(0.5000\ \mathrm{L}\) first.

\[ 0.250\ \mathrm{mol/L} \times 0.5000\ \mathrm{L} = 0.125\ \mathrm{mol} \]

Key idea: the liter unit cancels only when solution volume is written in liters.

Practice check

Calculate the mass of CaCl₂

What mass of CaCl₂ is needed to prepare \(250.0\ \mathrm{mL}\) of \(0.100\ \mathrm{M}\) CaCl₂?

Show answer and reasoning

Convert volume to liters:

\[ 250.0\ \mathrm{mL} = 0.2500\ \mathrm{L} \]

Find moles of CaCl₂:

\[ n_{\mathrm{CaCl_2}} = 0.100\ \mathrm{mol/L} \times 0.2500\ \mathrm{L} = 0.0250\ \mathrm{mol} \]

Use molar mass \(M_{\mathrm{CaCl_2}} = 110.98\ \mathrm{g/mol}\):

\[ m_{\mathrm{CaCl_2}} = 0.0250\ \mathrm{mol} \times 110.98\ \mathrm{g/mol} = 2.77\ \mathrm{g} \]

Answer: \(2.77\ \mathrm{g}\) CaCl₂.

Apply the topic

A reliable strategy for known-molarity mass problems

Step 1

Write the formula correctly

Use proper subscripts, such as NaCl, CaCl₂, or CuSO₄.

Step 2

Convert volume to liters

Molarity uses \(\mathrm{mol/L}\), so volume must be in L.

Step 3

Calculate moles

Use \(n = M \times V\).

Step 4

Convert to grams

Use \(m = n \times M_{\mathrm{molar}}\).

In real solution preparation, weigh the solute first, dissolve it in some water, then add water until the total solution volume reaches the target volume.

Summary

What to remember

Molarity means mol/L

\(M = \frac{n}{V}\), so \(n = M \times V\).

Volume must be in liters

Convert mL to L before calculating moles.

Molar mass gives grams

Use the correct formula and periodic table to find \(\mathrm{g/mol}\).

Mass is the final preparation amount

Dissolve that mass, then dilute to the final solution volume.

\[ m = M \times V_{\mathrm{L}} \times M_{\mathrm{molar}} \]