Q16.101P - Chemistry: Molecular Nature Of Matter And Change

Question

Question:For the decomposition of gaseous dinitrogen pentaoxide,

$2{\mathrm{N}}_{5\left(\mathrm{g}\right)} \to 4{\mathrm{NO}}_{2\left(\mathrm{g}\right)}+{\mathrm{O}}_{2\left(\mathrm{g}\right),}$the rate constant is k $=2.8\times {10}^{-3}{\mathrm{s}}^{-1 }\mathrm{at} 60°\mathrm{C}. \mathrm{The}$initial concentration  of ${\mathrm{N}}_2{\mathrm{O}}_5$is 1.58 mol/L. 

(a) What $\left[{\mathrm{N}}_2{\mathrm{O}}_5\right]$after 5.00 min?

(b) What fraction of the ${\mathrm{N}}_2{\mathrm{O}}_5$has decomposed after 5.00 min?

Step-by-Step Solution

Answer

$\left(\mathrm{a}\right)$After 5.00 min, the concentration is equal to 0.68 mol/L.  

  $\left(\mathrm{b}\right)$After5.00 min, the fraction of decomposed is equal to 0.57.

Step 1: Identify given information

From the problem: Question:For the decomposition of gaseous dinitrogen pentaoxide, 2 N 5 g → 4 NO 2 g + O 2 g , the rate constant is k = 2 . 8 × 10 - 3 s - 1 at 60 ° C . The initial concentration of N 2 O 5 is 1.58 mol/L. (a) What N 2 O 5 after 5.00 min ? (b) What fraction of the N 2 O 5 has decomposed after 5.00 min?

Step 2: Determine what to find

We identify the unknown quantity in this Chemistry problem and select the appropriate approach.

Step 3: Select the appropriate formula

Based on the given data and unknown, we choose the relevant equation from Chemistry.

Step 4: Substitute values and solve

Substituting known values into the equation, we perform the calculation.

Step 5: State the result

The result is: a After 5.00 min, the concentration is equal to 0.68 mol/L. b After5.00 min, the fraction of decomposed is equal to 0.57.