The decomposition of dimethyl ether leads to the formation of CH4, H2 and CO and the reaction rate is given by
\(Rate = k [CH_3OCH_3]^{\frac 32}\)
The rate of reaction is followed by increase in pressure in a closed vessel, so the rate can also be expressed in terms of the partial pressure of dimethyl ether, i.e.,
\(Rate = k(p_{CH_3OCH_3})^{\frac 32}\)
If the pressure is measured in bar and time in minutes, then what are the units of rate and rate constants?
The decomposition of dimethyl ether leads to the formation of CH4, H2 and CO and the reaction rate is given by
\(Rate = k [CH_3OCH_3]^{\frac 32}\)
The rate of reaction is followed by increase in pressure in a closed vessel, so the rate can also be expressed in terms of the partial pressure of dimethyl ether, i.e.,
\(Rate = k(p_{CH_3OCH_3})^{\frac 32}\)
If the pressure is measured in bar and time in minutes, then what are the units of rate and rate constants?
Solution and Explanation
\(If\ pressure \ is \ measured \ in\ bar\ and\ time \ in\ minutes\, \ then\)
\(Unit \ of\ rate = bar \ min^{-1}\)
\(Rate = k(p_{CH_3OCH_3})^{\frac 32}\)
\(k = \frac {Rate}{(p_{CH_3OCH_3})^{\frac 32}}\)
\(Therefore, \ unit\ of \ rate\ constants = \frac {bar \ min^{-1}}{bar^{\frac 32}}\)
= \(bar^{-\frac 12} min^{-1}\)
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Concepts Used:
Rate of a Chemical Reaction
The rate of a chemical reaction is defined as the change in concentration of any one of the reactants or products per unit time.
Consider the reaction A → B,
Rate of the reaction is given by,
Rate = −d[A]/ dt=+d[B]/ dt
Where, [A] → concentration of reactant A
[B] → concentration of product B
(-) A negative sign indicates a decrease in the concentration of A with time.
(+) A positive sign indicates an increase in the concentration of B with time.
Factors Determining the Rate of a Reaction:
There are certain factors that determine the rate of a reaction:
- Temperature
- Catalyst
- Reactant Concentration
- Chemical nature of Reactant
- Reactant Subdivision rate