To solve this problem, we need to analyze the given assertion and reason.$\\$Assertion A: In the equation $\Delta_r G = - nF E_{cell},$ the value of $\Delta_r G$ depends on $n. \\$Reason R: $E_{cell}$ is an intensive property and $\Delta_r G$ is an extensive property.$\\$Let's break down each part:$\\$• The equation $\Delta_r G = - nF E_{cell}$ is used to relate the Gibbs free energy change $\Delta_r G \\$ to the cell potential $E_{cell}. \\$• Here, $n$ is the number of moles of electrons transferred in the reaction, $F$ is Faraday's constant,$\\$ and $E_{cell}$ is the electromotive force (emf) of the cell.$\\$• $\Delta_r G$ is an extensive property, meaning it depends on the amount of substance involved.$\\$• $E_{cell}$ is an intensive property, meaning it does not depend on the amount of substance.$\\$Analyzing the assertion:$\\$• Since $\Delta_r G$ is calculated using $n$ (the number of moles of electrons), it is directly proportional to $n. \\$• Therefore, the assertion that $\Delta_r G$ depends on $n$ is true.$\\$Analyzing the reason:$\\$• $E_{cell}$ being an intensive property means it remains constant regardless of the system size.$\\$• $\Delta_r G$ being an extensive property means it scales with the size of the system or the amount of substance.$\\$• The reason correctly states the nature of these properties.$\\$Conclusion:$\\$• Both the assertion and the reason are true.$\\$• The reason correctly explains why $\Delta_r G$ depends on $n$ because $n$ affects the extensive property $\Delta_r G. \\$Therefore, the correct option is 1: Both A and R are true and R is the correct explanation of A.