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4.2: Limiting & Excess Reagents

  • Page ID
    51453
  • Learning Objectives

    • Understanding Stoichiometric Proportions
    • Understanding Limiting and Excess Reagents
      • Predict quantities of products produced or reactants consumed based on complete consumption of limiting reagent (on both mole and mass basis)
      • Predict quantities of excess reagents left over after complete consumption of limiting reagents.

    Stoichiometric Proportions and Theoretical Yield

    A balanced chemical equation describe the ratios at which products and reactants are respectively produced and consumed. That said, the coefficients of the balanced equation have nothing to do with the actual quantity of reactants you start with, as you can mix any amount you choose, but clearly the maximum yield (theoretical yield) must be limited by the reactant that gets consumed up first, the limiting reagent. Any reagents remaining after the complete consumption of the limiting reagent are know as excess reagents.

    Video \(\PageIndex{1}: 4/34" YouTube uploaded by "Professor Dave Explains", the first 2:47 goes over Limiting and excess reagents, and then it goes into Percent Yield (section 4.2.3)

    Here is some common terminology used to describe reactions based on the concentrations of reactions.

    • Stoichiometric Proportions: Reactants are mixed in the ratios defined by their stoichiometric coefficients. If a reaction proceeds to completion, everything is consumed.
    • NonStoichiometric Proportions: Reactants are mixed in ratios that are different than the stoichiometric coefficients. One species runs out first (Limiting Reagent), while another is not completely consumed (Excess Reagent).
      • Excess Reagent: The quantity (mole or mass) left over after the complete consumption of the limiting reagent

    Quantity Excess = Initial Quantity - Consumed Quantity.

    • Theoretical Yield: the maximum possible yield based on the complete consumption of the limiting reagent

    Thought Question \(\PageIndex{1}\)

    Are the limiting reagents always completely consumed?

    Answer

    No, only if the reaction goes to completion. There can be many different reasons why the limiting reagent is not completely consumed, these can include:

    • Products also react to form reactants causing an equilibrium of reactants of products to coexist, this will be covered next semester (see Chapter 15)
    • Reactions may not be over (some reactions occur very slowly).

    Limiting Reagent Problem Strategies:

    1. Identify moles of all reactants present.
      If given mass, divide by formula weight to convert to moles (this is the mass to mole step from the section 4.1,3.
    2. Divide moles of each reactant by it's stoichiometric coefficient.
      This is the denominator of the mole-to-mole step in section 4.1.3.
    3. Smallest number indicates limiting reagent.
    4. Multiply by stoichiometric coefficient of species you are solving for, and answer the question .
      This is the numerator of the mole-to-mole step in section 4.1.3. If you are after moles, you are finished, if you are after mass, you need to use the molar mass of product to convert moles product to grams mass product, which is the mass-to-mole step in section 4.1.

    Limiting Reagent Problem

    Silver tarnishes in the presence of hydrogen sulfide and oxygen due to the following reaction

    4Ag + 2H2S + O2 ----> 2Ag2S + 2H2O

    What is the Limiting Reagent and Theoretical Yield of Ag2S if 2.4 g Ag, 0.48 g H2S and 0.16g O2 react?

    Note in the video how we first wrote the balanced equation, and then under each species wrote down what we were given. In this problem there are 3 reagents, and this technique allows us to quickly identify the

    Video \(\PageIndex{2}\): 6'07" YouTube calculating the theoretical yield of Ag2S based on the complete consumption of the limiting reagent (https://youtu.be/26ieM_k0NOU) [Digital Corrigendum: @1'50" in the video the mass silver divided by its molar mass and stoiochiometric coefficient was written down to be 0.0556 but was 0.00556. at 2'22" the value of oxygen was determined to be 0.005, and so that was smaller and was the limiting reagent. Note: at 2:57 this problem is redone the long way, and this allows you to see how the shortcut works.

    Now calculate the excess reagents for the reaction of 2.4 g Ag, 0.48 g H2S and 0.16g O2 to form Ag2S + H2O.

    Video \(\PageIndex{3}\): 4'37" YouTube calculating the excess reagent concentrations when 2.4 g Ag, 0.48 g H2S and 0.16g O2 react.

    Exercise \(\PageIndex{1}\)

    Consider the oxidation of glucose through respiration:

    \[C_6H_{12}O_6 + 6O_2 \rightarrow 6CO_2+6H_2O + Energy\]

    What mass of carbon dioxide forms when 25.00 g of glucose reacts with 40.0 g of oxygen?

    Answer

    Step 1: Calculate moles of each reactant:

    \(\mathrm{25.00\:g \times \dfrac{1\: mol}{180.06\:g} = 0.1388\: mol\: C_6H_{12}O_6}\)

    \(\mathrm{40.0\:g \times \dfrac{1\: mol}{32\:g} = 1.25\: mol\: O_2}\)

    Step 2: Divide each by its stoichiometric coefficient, smallest value is limiting reagent.

    \[1.25 mol O_2(\frac{1}{6mol})=0.208 \\ 0.1388 mol C_6H_{12}O_6(\frac{1}{1mol})=0.1388 \]

    So glucose is the limiting reagent.

    Step 3: calculate the mass carbon dioxide based on the complete consumption of the limiting reagent.

    \[0.1388 mol \; C_6H_{12}O_6(\frac{6mol \; CO_2}{1mol \; C_6H_{12}O_6})\left ( \frac{44.011g\; CO_2}{mol} \right )=36.66g \; CO_2\]

    Contributors and Attributions

    Robert E. Belford (University of Arkansas Little Rock; Department of Chemistry). The breadth, depth and veracity of this work is the responsibility of Robert E. Belford, rebelford@ualr.edu. You should contact him if you have any concerns. This material has both original contributions, and content built upon prior contributions of the LibreTexts Community and other resources, including but not limited to:

    • Ronia Kattoum (UALR)
    • anonymous