Let's evaluate each option for the possibility of a chemical reaction:
1. Gold ornaments are washed with dil. HCl: - Gold (Au) is a noble metal and does not react with dilute hydrochloric acid (HCl). Therefore, no chemical reaction will occur in this case.
2. ZnSO\(_4\) (aq) is placed in a copper vessel:
Zinc sulfate (ZnSO\(_4\)) is an aqueous solution, and copper is less reactive than zinc. When zinc sulfate solution is placed in a copper vessel, no reaction occurs between zinc sulfate and the copper vessel. However, if the copper vessel was placed in a more reactive metal, such as zinc, a reaction could occur. But in this case, the metal zinc is reacting with the copper solution.
3. AgNO\(_3\) solution is stirred with a copper spoon:
Copper (Cu) is more reactive than silver (Ag), so when AgNO\(_3\) solution is stirred with a copper spoon, copper will displace silver from silver nitrate, forming copper nitrate and silver. The reaction is: \[ \text{Cu} + 2\text{AgNO}_3 \rightarrow \text{Cu(NO}_3)_2 + 2\text{Ag}. \] Therefore, a chemical reaction is possible.
4. Conc. HNO\(_3\) is stored in a platinum vessel:
Platinum is an inert metal and does not react with concentrated nitric acid (HNO\(_3\)). Therefore, no reaction occurs in this case.
Thus, the correct answer is (B) ZnSO\(_4\) (aq) is placed in a copper vessel, as it is the only option where a chemical reaction is possible.
In option (C), AgNO3 reacts with the copper spoon because copper displaces silver from the silver nitrate solution. The reaction is: \[ \text{Cu} + 2\text{AgNO}_3 \rightarrow \text{Cu(NO}_3)_2 + 2\text{Ag} \] In other options, no such reaction occurs due to the nature of the metals and solutions involved. Gold is unreactive with dilute HCl, zinc sulfate does not react with copper, and platinum is inert towards concentrated nitric acid.
The speed at which a chemical reaction takes place is called the rate of reaction. The rate of reaction depends on various factors like concentration of the reactants, temperature, etc. The relation between the rate of reaction and the concentration of reacting species is represented by the equation \( r = k[A]^x[B]^y \), where \( x \) and \( y \) are the order of the reaction with respect to the reactants A and B, respectively. The overall order of the reaction is \( x + y \). The rate of reaction can also be increased by the use of a catalyst which provides an alternate pathway of lower activation energy. It increases the rate of forward and backward reactions to an equal extent. It does not alter the Gibbs energy of the reaction.
Match the following:
In the following, \( [x] \) denotes the greatest integer less than or equal to \( x \). 
Choose the correct answer from the options given below:
For x < 0:
f(x) = ex + ax
For x ≥ 0:
f(x) = b(x - 1)2
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.
There are certain factors that determine the rate of a reaction: