Respuesta :
The rates of production of [tex]{{\text{P}}_4}[/tex] and [tex]{{\text{H}}_{\text{2}}}[/tex] are [tex]0.00325{\text{ mol}} \cdot {{\text{L}}^{ - 1}} \cdot {{\text{s}}^{ - 1}}[/tex] and [tex]0.0195{\text{ mol}} \cdot {{\text{L}}^{ - 1}} \cdot {{\text{s}}^{ - 1}}[/tex] respectively.
Further Explanation:
The rate of reaction is the pace at which reactants get converted into products. A general chemical reaction can be written as follows:
[tex]{\text{aA}} + {\text{bB}} \to {\text{cC}} + {\text{dD}}[/tex]
Here,
A and B are the reactants.
C and D are the products.
a and b are the stoichiometric coefficients of reactants.
c and d are the stoichiometric coefficients of products.
The expression for the rate of reaction for the above equation is as follows:
[tex]{\text{Rate of reaction}} = - \dfrac{1}{{\text{a}}}\dfrac{{d\left[ {\text{A}} \right]}}{{dt}} = - \dfrac{1}{{\text{b}}}\dfrac{{d\left[ {\text{B}} \right]}}{{dt}} = \dfrac{1}{{\text{c}}}\dfrac{{d\left[ {\text{C}} \right]}}{{dt}} = \dfrac{1}{{\text{d}}}\dfrac{{d\left[ {\text{D}} \right]}}{{dt}}[/tex]
Here, negative sign indicates the consumption of reactants whereas positive sign depicts the formation of products.
The given reaction is as follows:
[tex]4{\text{P}}{{\text{H}}_{\text{3}}}\left( g \right) \to {{\text{P}}_{\text{4}}}\left( g \right) + 6{{\text{H}}_{\text{2}}}\left( g \right)[/tex]
The expression for rate of reaction for the given reaction is as follows:
[tex]{\text{Rate of reaction}}= - \dfrac{1}{4}\dfrac{{d\left[ {{\text{P}}{{\text{H}}_{\text{3}}}} \right]}}{{dt}} = \dfrac{{d\left[ {{{\text{P}}_{\text{4}}}} \right]}}{{dt}} = \dfrac{1}{6}\dfrac{{d\left[ {{{\text{H}}_2}} \right]}}{{dt}}[/tex] …… (1)
Here,
[tex]\dfrac{{d\left[ {{\text{P}}{{\text{H}}_{\text{3}}}} \right]}}{{dt}}[/tex] is the rate of consumption of [tex]{\text{P}}{{\text{H}}_{\text{3}}}[/tex].
[tex]\dfrac{{d\left[ {{{\text{P}}_{\text{4}}}} \right]}}{{dt}}[/tex] is the rate of formation of [tex]{{\text{P}}_{\text{4}}}[/tex].
[tex]\dfrac{{d\left[ {{{\text{H}}_2}} \right]}}{{dt}}[/tex] is the rate of formation of [tex]{{\text{H}}_2}[/tex].
The rate of decomposition of [tex]{\text{P}}{{\text{H}}_{\text{3}}}[/tex] can be determined as follows:
[tex]\begin{aligned}{\text{Rate of decomposition of P}}{{\text{H}}_{\text{3}}} &= \frac{{0.065{\text{ mol/s}}}}{{5{\text{ L}}}}\\&= 0.013{\text{ mol}} \cdot {{\text{L}}^{ - 1}} \cdot {{\text{s}}^{ - 1}}\\\end{aligned}[/tex]
The formula to calculate the rate of production of [tex]{{\text{P}}_4}[/tex] is as follows:
[tex]{\text{Rate of production of }}{{\text{P}}_4} = \frac{1}{4}\left( {{\text{Rate of decomposition of P}}{{\text{H}}_{\text{3}}}} \right)[/tex] …… (2)
The rate of decomposition of [tex]{\text{P}}{{\text{H}}_{\text{3}}}[/tex] is [tex]0.013{\text{ mol}} \cdot {{\text{L}}^{ - 1}} \cdot {{\text{s}}^{ - 1}}[/tex]. Substitute this value in equation (2).
[tex]\begin{aligned}{\text{Rate of production of }}{{\text{P}}_4} &= \frac{1}{4}\left( {0.013{\text{ mol}} \cdot {{\text{L}}^{ - 1}} \cdot {{\text{s}}^{ - 1}}} \right)\\&= 0.00325{\text{ mol}} \cdot {{\text{L}}^{ - 1}} \cdot {{\text{s}}^{ - 1}}\\\end{aligned}[/tex]
Therefore the rate of production of [tex]{{\text{P}}_{\text{4}}}[/tex] is [tex]0.00325{\text{ mol}} \cdot {{\text{L}}^{ - 1}} \cdot {{\text{s}}^{ - 1}}[/tex].
The formula to calculate the rate of production of [tex]{{\text{H}}_{\text{2}}}[/tex] is as follows:
[tex]{\text{Rate of production of }}{{\text{H}}_{\text{2}}} = \dfrac{6}{4}\left( {{\text{Rate of decomposition of P}}{{\text{H}}_{\text{3}}}} \right)[/tex] …… (3)
The rate of decomposition of [tex]{\text{P}}{{\text{H}}_{\text{3}}}[/tex] is [tex]0.013{\text{ mol}} \cdot {{\text{L}}^{ - 1}} \cdot {{\text{s}}^{ - 1}}[/tex]. Substitute this value in equation (3).
[tex]\begin{aligned}{\text{Rate of production of }}{{\text{H}}_{\text{2}}}&= \frac{6}{4}\left( {0.013{\text{ mol}} \cdot {{\text{L}}^{ - 1}} \cdot {{\text{s}}^{ - 1}}} \right)\\&= 0.0195{\text{ mol}} \cdot {{\text{L}}^{ - 1}} \cdot {{\text{s}}^{ - 1}} \\ \end{aligned}[/tex]
Therefore the rate of production of [tex]{{\text{H}}_2}[/tex] is [tex]0.0195{\text{ mol}} \cdot {{\text{L}}^{ - 1}} \cdot {{\text{s}}^{ - 1}}[/tex].
Learn more:
- Rate of chemical reaction: https://brainly.com/question/1569924
- The main purpose of conducting experiments: https://brainly.com/question/5096428
Answer Details:
Grade: Senior School
Chapter: Chemical Kinetics
Subject: Chemistry
Keywords: PH3, P4, H2, rate of formation, rate of decomposition, rate of reaction, 0.013 mol/L/s, 0.0195 mol/L/s, 0.00325 mol/L/s, rate of consumption, negative sign, positive sign.
