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Consider the reaction described by the following equation c2h4br2(aq)

Consider the reaction described by the following equation.

C2H4Br2(aq)+3I^-(aq) ----->  C2H4(g)+2Br^-(aq)+i(negative charge)(three subscript) (aq)

The rate law is

rate = k[C2H4Br2] [I^-]        Where k=4.77x10^-3 M^-1 s^-1

What are the missing entries in the following table?

Run    [C2H4Br2]0(M)     [I^-]0(M)     Initial rate of formation of C2H4(M s^-1

_____________________________________________________

1                x                        0.299          0.00100

2                0.299                 y                 0.000500

3                0.299                 0.299          z

x=_____M     y=_________M       z=________M s^-1

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Answer #1

General guidance

Concepts and reason

The concept used to solve this problem is based on how rate of a reaction is dependent on several factors in chemical kinetics. According to the Law of mass action the rate of a reaction is proportional to the concentration of the reactants.Given the rate law for the reaction, each missing part can be obtained by substituting the other known values in the rate law.

Fundamentals

Rate law is an equation which relates the rate of a reaction and the concentration of the reactants. For a general reaction, A+B\u2192C{\\rm{A + B}} \\to {\\rm{C}}the rate law is given by

r=k[A]x[B]y{\\rm{r}} = k{\\left[ {\\rm{A}} \\right]^{\\rm{x}}}{\\left[ {\\rm{B}} \\right]^{\\rm{y}}}

Where,[A]\\left[ {\\rm{A}} \\right]and [B]\\left[ {\\rm{B}} \\right]are concentrations of the reactants; x and y are the orders of reaction and k is the reaction constant.

Step-by-step

Step 1 of 3

Part a

Given that the rate law of the mentioned reaction is

rate=k[C2H4Br2][I]{\\rm{rate = }}k\\left[ {{{\\rm{C}}_{\\rm{2}}}{{\\rm{H}}_{\\rm{4}}}{\\rm{B}}{{\\rm{r}}_{\\rm{2}}}} \\right]\\left[ {\\rm{I}} \\right] \u2026\u2026 (1)

Rearrange the equation for obtaining [C2H4Br2]\\left[ {{{\\rm{C}}_{\\rm{2}}}{{\\rm{H}}_{\\rm{4}}}{\\rm{B}}{{\\rm{r}}_{\\rm{2}}}} \\right]

[C2H4Br2]=ratek[I]\\left[ {{{\\rm{C}}_{\\rm{2}}}{{\\rm{H}}_{\\rm{4}}}{\\rm{B}}{{\\rm{r}}_{\\rm{2}}}} \\right] = \\frac{{{\\rm{rate}}}}{{k\\left[ {\\rm{I}} \\right]}}

Substitute 0.299M for[I]\\left[ {\\rm{I}} \\right], 0.00100Ms\u221210.00100{\\rm{ M }}{{\\rm{s}}^{ - 1}} for rate and 4.77\u00d710\u22123M\u22121s\u221214.77 \\times {10^{ - 3}}{{\\rm{M}}^{{\\rm{ - 1}}}}{{\\rm{s}}^{{\\rm{ - 1}}}}for k in the above expression as follows:

[C2H4Br2]=ratek[I]=0.001Ms\u22121(4.77\u00d710\u22123M\u22121s\u22121)(0.299M)=0.7011M\\begin{array}{c}\\\\\\left[ {{{\\rm{C}}_{\\rm{2}}}{{\\rm{H}}_{\\rm{4}}}{\\rm{B}}{{\\rm{r}}_{\\rm{2}}}} \\right] = \\frac{{{\\rm{rate}}}}{{k\\left[ {\\rm{I}} \\right]}}\\\\\\\\ = \\frac{{0.001{\\rm{ \\bcancel{M} }}{{{\\rm{\\bcancel{s}}}}^{{\\rm{ - 1}}}}}}{{\\left( {4.77 \\times {{10}^{ - 3}}{\\rm{ }}{{\\rm{M}}^{{\\rm{ - 1}}}}{\\rm{ }}{{{\\rm{\\bcancel{s}}}}^{{\\rm{ - 1}}}}} \\right)\\left( {0.299{\\rm{ \\bcancel{M}}}} \\right)}}\\\\\\\\ = 0.7011{\\rm{ M}}\\\\\\end{array}

The concentration of C2H4Br2{{\\rm{C}}_{\\rm{2}}}{{\\rm{H}}_{\\rm{4}}}{\\rm{B}}{{\\rm{r}}_{\\rm{2}}} is 0.7011M.

Part a

Concentration of C2H4Br2{{\\rm{C}}_{\\rm{2}}}{{\\rm{H}}_{\\rm{4}}}{\\rm{B}}{{\\rm{r}}_{\\rm{2}}} is 0.7011M.


Explanation | Common mistakes | Hint for next step

For the first run, the concentration of iodide and rate of formation are known. From these known values, unknown concentration of C2H4Br2{{\\rm{C}}_{\\rm{2}}}{{\\rm{H}}_{\\rm{4}}}{\\rm{B}}{{\\rm{r}}_{\\rm{2}}}is calculated using the rate law.

Step 2 of 3

Part b

Rearrange equation (1) for[I]\\left[ {\\rm{I}} \\right]

[I]=ratek[C2H4Br2]\\left[ {\\rm{I}} \\right] = \\frac{{{\\rm{rate}}}}{{k\\left[ {{{\\rm{C}}_{\\rm{2}}}{{\\rm{H}}_{\\rm{4}}}{\\rm{B}}{{\\rm{r}}_{\\rm{2}}}} \\right]}}

Substitute 0.299M for[C2H4Br2]\\left[ {{{\\rm{C}}_{\\rm{2}}}{{\\rm{H}}_{\\rm{4}}}{\\rm{B}}{{\\rm{r}}_{\\rm{2}}}} \\right]

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