The phrase how to find molarity refers to computing the molarity (also called molar concentration) of a solution: the number of moles of solute per liter of solution.
Definition: \[ M = \frac{n_{\text{solute}}}{V_{\text{solution}}} \] where \(M\) is molarity in \(\mathrm{mol/L}\), \(n_{\text{solute}}\) is moles of solute in \(\mathrm{mol}\), and \(V_{\text{solution}}\) is solution volume in \(\mathrm{L}\).
1) Core method: the three required conversions
- Ensure the volume is in liters. Convert mL to L using \(1\,\mathrm{L} = 1000\,\mathrm{mL}\), so \[ V(\mathrm{L}) = \frac{V(\mathrm{mL})}{1000}. \]
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Determine moles of solute. Common routes:
Given Find moles using Notes Mass \(m\) (g) \[ n = \frac{m}{M_\mathrm{m}} \] \(M_\mathrm{m}\) is molar mass in \(\mathrm{g/mol}\). Moles \(n\) (mol) \[ n = n \] No conversion needed. Particles \(N\) \[ n = \frac{N}{N_\mathrm{A}} \] \(N_\mathrm{A} = 6.022 \times 10^{23}\,\mathrm{mol^{-1}}\). Gas data \(P, V, T\) \[ n = \frac{P \times V}{R \times T} \] Use \(V\) in liters and \(T\) in kelvin with consistent \(R\). - Compute molarity by division. \[ M = \frac{n}{V}. \]
2) Visualization: flow of steps to find molarity
3) Worked example (mass given)
A solution is prepared by dissolving \(5.85\,\mathrm{g}\) of \(\mathrm{NaCl}\) and diluting to a final volume of \(500.0\,\mathrm{mL}\). Find the molarity.
Step 1: Convert volume to liters
\[ V = \frac{500.0\,\mathrm{mL}}{1000} = 0.5000\,\mathrm{L}. \]Step 2: Convert grams to moles
Molar mass: \[ M_\mathrm{m}(\mathrm{NaCl}) = 22.99 + 35.45 = 58.44\,\mathrm{g/mol}. \] Moles: \[ n = \frac{5.85\,\mathrm{g}}{58.44\,\mathrm{g/mol}} = 0.1001\,\mathrm{mol}. \]
Step 3: Compute molarity
\[ M = \frac{0.1001\,\mathrm{mol}}{0.5000\,\mathrm{L}} = 0.2002\,\mathrm{mol/L}. \]With appropriate significant figures, \(M \approx 0.200\,\mathrm{M}\).
4) Common mistakes when finding molarity
- Not converting to liters: molarity is \(\mathrm{mol/L}\), so \(V\) must be in \(\mathrm{L}\).
- Using solvent volume instead of solution volume: molarity uses the final volume of the solution.
- Forgetting units in conversions: keep \(\mathrm{g}\), \(\mathrm{mol}\), \(\mathrm{mL}\), \(\mathrm{L}\) visible until they cancel correctly.
- Mixing dilution ideas prematurely: when a solution is made by diluting to a mark, the final volume is the one used in \(M = n/V\).
The essential result for how to find molarity is the definition \( M = \frac{n}{V} \): convert solute amount to moles, convert solution volume to liters, then divide to obtain \(\mathrm{mol/L}\).