solve this problem---**Question Stem:**
Consider a reaction A(g) --k=0.1 M min⁻¹--> 2B(g). If initial concentration of A is 0.5M then select correct graph.
**Options:**
**(a)**
Chart Type: Line chart
X-axis: time (in min), scale marked at 5, 10.
Y-axis: [B], scale marked at 0.5M.
Line: Starts at (0, 0), increases linearly up to (5, 0.5M), then becomes horizontal at 0.5M.
**(b)**
Chart Type: Line chart
X-axis: time (in min), scale marked at 5, 10.
Y-axis: [B], scale marked at 0.5M, 1.0M.
Line: Starts at (0, 0), increases linearly, passes through approximately (5, 0.5M) and (10, 1.0M).
**(c)**
Chart Type: Line chart
X-axis: time (in min), scale marked at 5, 10.
Y-axis: [B], scale marked at 1.0M.
Line: Starts at (0, 0), increases linearly up to (5, 1.0M), then becomes horizontal at 1.0M.
**(d)**
Chart Type: Line chart
X-axis: time (in min), scale marked at 5, 10.
Y-axis: [B], scale marked at 1.0M, 2.0M.
Line: Starts at (0, 0), increases linearly, passes through approximately (5, 1.0M) and (10, 2.0M).
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We have a chemical reaction where A converts to 2B with rate constant 0.1 M per minute. The initial concentration of A is 0.5 M. The units of the rate constant tell us this is a zero-order reaction. Let's analyze this step by step.
For a zero-order reaction, the rate is constant and independent of reactant concentration. The rate law shows that A decreases at 0.1 M per minute. Using stoichiometry, since one mole of A produces two moles of B, the rate of B formation is twice the rate of A consumption, which equals 0.2 M per minute.
Now let's calculate the key parameters. For zero-order kinetics, A concentration decreases linearly. Setting A equal to zero, we find that A is completely consumed after 5 minutes. From stoichiometry, 0.5 M of A produces 1.0 M of B. The concentration of B increases linearly at 0.2 M per minute until all A is consumed.
The graph shows concentration of B versus time. B starts at zero and increases linearly with slope 0.2 M per minute until t equals 5 minutes, reaching 1.0 M. After 5 minutes, all A is consumed, so the reaction stops and B concentration remains constant at 1.0 M. This matches option C from the multiple choice answers.
In conclusion, the correct answer is option C. The graph shows B concentration increasing linearly from zero to 1.0 M over 5 minutes, then remaining constant. This matches our calculated behavior for the zero-order reaction where A is completely consumed after 5 minutes, producing exactly 1.0 M of product B.