Lab Math: Concentration Calculations in the Laboratory

Lab Math: Concentration Calculations

Introduction to Concentration Calculations

  • Focus on concentration calculations in laboratory settings.

  • Types of percent concentrations discussed:

    • Percent weight per weight (w/w)

    • Percent weight per volume (w/v)

    • Percent volume per volume (v/v)

  • Total volume of the solvent for calculations is based on 100 mL or 100 grams, contrasting with molarity or normality used with 1.0 liters.

1. Percent Weight per Weight (w/w)

  • Definition: Percent weight per weight is calculated using the formula:
    extPercentw/w=racextgramsofsolute100extgramsofsolutionext{Percent w/w} = rac{ ext{grams of solute}}{100 ext{ grams of solution}}

  • Explanation of measurement: Both solute and solvent must be weighed separately using a balance.

  • Formula Explanation:

    • Amount of solute in 100 grams of solution

    • Total weight of the solution (solute + solvent) = 100 grams.

  • If the weight of the solute is known, the weight of the solvent can be determined by:
    extWeightofsolvent=100extgrams−extWeightofsoluteext{Weight of solvent} = 100 ext{ grams} - ext{Weight of solute}

  • Mixing: Combine solute and solvent in a beaker or flask. Deionized water is typically used as a solvent.

  • Accuracy: Percent w/w is generally more accurate than percent w/v since it is not affected by temperature variations.

Example Calculation: Sodium Hydroxide Solution

  • Problem: How many grams of sodium hydroxide (NaOH) are required to create a 30% w/w solution?

    • Formula: Percent w/w = grams of solute / 100 grams of solution

    • Plugging values into formula:
      30 ext{%} = rac{x ext{ grams of NaOH}}{100 ext{ grams of solution}}

    • Cross multiplication gives:
      x=30extgramsofNaOHx = 30 ext{ grams of NaOH}

  • To make the solution, calculate the amount of deionized water needed: extTotalsolutionweight=extWeightofsolute+extWeightofsolventext{Total solution weight} = ext{Weight of solute} + ext{Weight of solvent} 100=30+extWeightofsolvent100 = 30 + ext{Weight of solvent}

    • Therefore, 70 grams of deionized water is required.

2. Percent Weight per Volume (w/v)

  • Definition: Calculated as follows:
    extPercentw/v=racextgramsofsolute100extmLofsolutionext{Percent w/v} = rac{ ext{grams of solute}}{100 ext{ mL of solution}}

  • Total volume instead of weight is used. Commonly found in clinical labs.

  • Procedure:

    • Weigh the solute and place it into a volumetric flask, initially adding a small amount of solvent to help dissolve the solute.

    • Add remaining solvent up to the 100 mL calibration mark of the flask.

  • The term quantitas sufficit (QS) refers to filling the volumetric flask to the calibration mark.

Example Calculation: Sodium Chloride Solution

  • Problem: What is the percent weight per volume of a solution with 25 grams of sodium chloride (NaCl) dissolved in a total volume of 100 mL?

    • Plugging into formula:
      extPercentw/v=rac25extgrams100extmLext{Percent w/v} = rac{25 ext{ grams}}{100 ext{ mL}}

    • Result:
      The solution has a 25% weight per volume concentration.

  • Preparation Steps:

    • Weigh 25 grams of NaCl.

    • Add to a volumetric flask partially filled with deionized water.

    • Dissolve and fill to the 100 mL mark to create the solution.

3. Percent Volume per Volume (v/v)

  • Definition: Calculated using the formula:
    extPercentv/v=racextmLofsolute100extmLofsolutionext{Percent v/v} = rac{ ext{mL of solute}}{100 ext{ mL of solution}}

  • Similar to weight per volume, both solute and solvent are measured in volume (mL).

  • Example: To calculate how much solvent is needed for a percentage volume solution:
    extAmountofsolvent=100extmL(totalvolume)−extAmountofsoluteext{Amount of solvent} = 100 ext{ mL (total volume)} - ext{Amount of solute}

Example Calculation: Ethanol Solution

  • Problem: How many mL of ethanol are needed to make a 75% volume for volume solution?

    • Using the formula:
      extPercentv/v=racxextmL100extmLext{Percent v/v} = rac{x ext{ mL}}{100 ext{ mL}} with desired percent = 75%

    • Solution results in:
      x=75extmLofethanolx = 75 ext{ mL of ethanol}

  • Final Calculation for Water:

    • To find mL of deionized water required:
      extWater=100−75=25extmLext{Water} = 100 - 75 = 25 ext{ mL}

4. Conversion of Percent Calculations to Molarity

  • Understanding Molarity: Molarity is calculated in moles per liter.

  • Example: Convert a 0.85% w/v sodium chloride solution to molarity.

    • The formula gives:
      0.85extgNaCl=rac0.85extg100extmL0.85 ext{ g NaCl} = rac{0.85 ext{ g}}{100 ext{ mL}}

  • To find concentration in 1 liter (1000 mL):

    • Cross-multiply to find grams in 1000 mL:
      0.85extgimes10=8.5extg0.85 ext{ g} imes 10 = 8.5 ext{ g}

  • Using Molar Mass: The molar mass of sodium chloride is 58.44 g/mol.

  • Molarity calculation: extMolarity=rac8.5extgNaCl58.44extg/molimesrac11extLext{Molarity} = rac{8.5 ext{ g NaCl}}{58.44 ext{ g/mol}} imes rac{1}{1 ext{ L}}

    • Result: Molarity is 0.14 M (moles per liter).

5. Concentration Calculations for Dilution

  • Dilution Formula: C<em>1V</em>1=C<em>2V</em>2C<em>1 V</em>1 = C<em>2 V</em>2 where:

    • $C_1$: concentration of the stock solution

    • $V_1$: volume of stock required

    • $C_2$: desired concentration

    • $V_2$: final total volume needed

  • Example Calculation:

    • Need to create 350 mL of a 2% solution from a 5% solution.

    • Using the equation:

    1. Plug values:
      5ext(C1)imesV1=2ext(C2)imes350ext(V2)5 ext{ (C1)} imes V_1 = 2 ext{ (C2)} imes 350 ext{ (V2)}

    2. This leads to:
      2imes350=7002 imes 350 = 700

    3. Solve for $V1$: 5V</em>1=7005V</em>1 = 700 → V1=140extmLV_1 = 140 ext{ mL}

  • Dilution Steps: Measure out 140 mL of the stock solution and dilute it to a total volume of 350 mL using deionized water to make the desired 2% solution of sodium chloride.