Chemical Kinetics

Step 1: Use stoichiometric rate relation.
For the reaction:
2A + B → C + D
Rate = −(1/2) d[A]/dt = d[C]/dt.
Step 2: Substitute given rate of consumption of A.
Given: −d[A]/dt = 0.1 mol L s .
Step 3: Apply stoichiometric coefficient.
d[C]/dt = (1/2)(0.1) = 0.05 mol L s .
Step 4: Conclusion.
Thus, the rate of formation of C is 0.05 mol L s .

Step 1: Write rate equations for each species.
For the given consecutive first-order reactions: Rate equations are: Step 2: Solve for .
Integrating the first equation: Step 3: Substitute into Y’s rate equation.
This is a linear first-order differential equation. Using the integrating factor : Integrating both sides: Step 4: Simplify to get .
Step 5: Conclusion.
Hence, the correct expression for the concentration of Y at time is: which corresponds to **Option (A)**.

Step 1: Write the rate expression using steady-state approximation. At steady state for the intermediate , Step 2: Rate of product formation. Hence, the effective rate constant: Step 3: Substitute the values. Step 4: Conclusion. Effective rate constant .

Step 1: RMS speed formula.
For gases at the same temperature,
Step 2: Apply for H and N .
Step 3: Conclusion.
RMS speed of N = 508 m s .

Step 1: Relation between half-life and concentration.
For a general reaction of order , Step 2: Compare ratios.
Let us compare two data points:
When changes from to , and Step 3: Apply proportionality.
Taking logarithms: Step 4: Conclusion.
Hence, the reaction is of second order.