Question

For gaseous reaction, the rate is often expressed in terms of \[\dfrac{dP}{dt}\] instead of \[\dfrac{dc}{dt}\] or \[\dfrac{dn}{dt}\] (where c is the concentration and n the number of mol). What is the relation among these three expressions?
A. $\dfrac{{dc}}{{dT}} = \dfrac{1}{V}\left( {\dfrac{{dn}}{{dT}}} \right) = \dfrac{1}{{RT}}\left( {\dfrac{{dP}}{{dT}}} \right)$
B. $\dfrac{{dc}}{{dT}} = \left( {\dfrac{{dn}}{{dT}}} \right) = \left( {\dfrac{{dP}}{{dT}}} \right)$
C. $\dfrac{{dc}}{{dT}} = \dfrac{1}{V}\left( {\dfrac{{dn}}{{dT}}} \right) = \dfrac{V}{{RT}}\left( {\dfrac{{dP}}{{dT}}} \right)$
D.None of these

Answer 1

Hint: We need to know that an ideal gas is a hypothetical gas made out of a bunch of arbitrarily moving point particles that associate just through versatile collisions.The ideal gas idea is helpful on the grounds that it complies with the ideal gas law, an improved condition of state, and is amiable to analysis under statistical mechanics.

Complete step by step answer:
We need to remember that the laws which manage ideal gases are normally called ideal gas laws and the laws controlled by the observational work of Boyle in the seventeenth century and Charles in the eighteenth century. The Ideal gas law is the condition of a theoretical ideal gas. It is a decent estimation to the conduct of numerous gases under numerous conditions, in spite of the fact that it has a few constraints. The ideal gas condition can be composed as,
$PV = nRT$
Here, P represents the pressure of ideal gas
V represents the volume of ideal gas
n represents the quantity of ideal gas (measured in moles)
R represents the Universal gas constant
T represents the Temperature
Based on Ideal Gas equation, the product of Pressure and volume has a constant region with the product of Universal gas constant and Temperature i.e $PV = nRT$
We know that concentration is the number of moles in one litre of solution. The equation could be given as,
$c = \dfrac{n}{V} = \dfrac{P}{{RT}}$
Differentiating the above equation we get,
$ \Rightarrow \dfrac{{dc}}{{dT}} = \dfrac{1}{V}\dfrac{{dn}}{{dt}} = \dfrac{1}{{RT}}\dfrac{{dP}}{{dt}}$
The relation among these three expressions is $\dfrac{{dc}}{{dT}} = \dfrac{1}{V}\dfrac{{dn}}{{dt}} = \dfrac{1}{{RT}}\dfrac{{dP}}{{dt}}$.

So, the correct answer is Option A.

Note: We need to know that for ideal gas conditions note that $PV$ is straightforwardly related to temperature. This implies that if the gas' temperature stays consistent, weight or volume can increment as long as the reciprocal variable abatements; this likewise implies that if the gas' temperature transforms, it could be expected to a limited extent to an adjustment in the variable of weight or volume.