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The table below shows recorded concentration data for the following chemical reaction:
\[{\text{CaC}}{{\text{l}}_{\text{2}}}_{\left( {{\text{aq}}} \right)}{\text{ + 2AgN}}{{\text{O}}_{\text{3}}}_{\left( {{\text{aq}}} \right)} \to {\text{Ca}}{\left( {{\text{N}}{{\text{O}}_{\text{3}}}} \right)_{\text{2}}}_{\left( {{\text{aq}}} \right)}{\text{ + 2AgC}}{{\text{l}}_{\left( {\text{s}} \right)}}\]
Use the data to determine the exponents x and y in the rate law:
\[{\text{Rate = k}}{\left[ {{\text{CaC}}{{\text{l}}_{\text{2}}}} \right]^{\text{x}}}{\left[ {{\text{AgN}}{{\text{O}}_{\text{3}}}} \right]^{\text{y}}}\]
\[\left[ {{\text{CaC}}{{\text{l}}_{\text{2}}}} \right]{\text{M}}\left[ {{\text{AgN}}{{\text{O}}_{\text{3}}}} \right]{\text{M}}\] rate
\[0.050\] \[0.050\] \[3.33 \times {10^{ - 3}}\]
\[0.100\] \[0.050\] \[6.66 \times {10^{ - 3}}\]
\[0.100\] \[0.100\] \[13.32 \times {10^{ - 3}}\]

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Last updated date: 19th Jul 2024
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Answer
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Hint: We have to remember that the rate of the reaction is an important factor for the study of reaction. The rate of reaction is an important concept for the chemical kinetics. Rate of the reaction depends on the concentration of the reactant. The rate of reaction is also calculated by using the concentration of the product in the chemical reaction. Depending on the concentration, the sign of the rate will change.
Formula used:
The rate of the reaction is directly proportional to the concentration of reactant and inversely proportional to the time of the reaction.
The rate of the reaction is equal to the product of the concentration of the reactant with respect to that order of the reaction.
\[{\text{rate = k[A}}{{\text{]}}^{\text{m}}}{{\text{[B]}}^{\text{n}}}\]
Here, k is proportionality constant, known as rate constant.
A and B are reactants of the reaction.
m and n are the order of the reaction of A and B respectively.

Complete answer:
The given chemical reaction is
\[{\text{CaC}}{{\text{l}}_{\text{2}}}_{\left( {{\text{aq}}} \right)}{\text{ + 2AgN}}{{\text{O}}_{\text{3}}}_{\left( {{\text{aq}}} \right)} \to {\text{Ca}}{\left( {{\text{N}}{{\text{O}}_{\text{3}}}} \right)_{\text{2}}}_{\left( {{\text{aq}}} \right)}{\text{ + 2AgC}}{{\text{l}}_{\left( {\text{s}} \right)}}\]
Use the data to determine the exponents x and y in the rate law:
\[{\text{Rate = k}}{\left[ {{\text{CaC}}{{\text{l}}_{\text{2}}}} \right]^{\text{x}}}{\left[ {{\text{AgN}}{{\text{O}}_{\text{3}}}} \right]^{\text{y}}}\]
\[\left[ {{\text{CaC}}{{\text{l}}_{\text{2}}}} \right]{\text{M}}\left[ {{\text{AgN}}{{\text{O}}_{\text{3}}}} \right]{\text{MrateM/s}}\]
\[0.050\] \[0.050\] \[3.33 \times {10^{ - 3}}\]
\[0.100\] \[0.050\] \[6.66 \times {10^{ - 3}}\]
\[0.100\] \[0.100\] \[13.32 \times {10^{ - 3}}\]
When the concentration of silver nitrate is constant, increasing the concentration of calcium chloride is double means, the rate of the reaction also two times increases.
\[0.050\] \[0.050\] \[3.33 \times {10^{ - 3}}\]
\[0.100\] \[0.050\] \[6.66 \times {10^{ - 3}}\]
Here, x represents the order of calcium chloride. Hence order of calcium chloride in the reaction is one. The value of x is\[1\].
When both the concentration of calcium chloride and silver nitrate doubles, the rate of reaction increases four times.
\[0.050\] \[0.050\] \[3.33 \times {10^{ - 3}}\]
\[0.100\] \[0.050\] \[6.66 \times {10^{ - 3}}\]
Hence, the order of both reactants is one. Y represents the order of silver nitrate. Both x and y are one.
The value of \[{\text{x = 1 and y = 1}}\].

Note:
We have to remember that the chemical formula of calcium chloride is \[{\text{CaC}}{{\text{l}}_{\text{2}}}\]. The chemical formula of silver nitrate is \[{\text{AgN}}{{\text{O}}_{\text{3}}}\]. The rate of the reaction depends on the initial concentration of the reactants in the chemical reaction. The rate of the reaction is used to measure decrease in the concentration of reactant and increase the concentration of the product in the reaction. The order of reaction may be fractional or integer or zero.