The decomposition of N_(2)O_(5)(g) is a first order reaction with a rate constant of 5xx10^(-4)s^(-1) at 45^(@)C. i.e., 2N_(2)O_(5)(g) to 4NO_(2)(g)+O_(2)(g). If initial concentrationof N_(2)O_(5) is 0.25M, calculate its concentration after 2 minutes. Also calculate the half-life for decomposition of N_(2)O_(5)(g).

The decomposition of N_(2)O_(5)(g) is a first order reaction with a ra

1.	The decomposition of N_(2)O_(5)(g) is a first order reaction with a rate constant of 5xx10^(-4)s^(-1) at 45^(@)C. i.e., 2N_(2)O_(5)(g) to 4NO_(2)(g)+O_(2)(g). If initial concentrationof N_(2)O_(5) is 0.25M, calculate its concentration after 2 minutes. Also calculate the half-life for decomposition of N_(2)O_(5)(g).
Answer» Solution :`K=5xx10^(-4)s^(-1), [R]_(0)=0.25 M, t=2xx60=120s` Use the relation, `k=(2.303)/(t)"log"([R]_(0))/([R])` Substituting the values, we get `5xx10^(-4)s^(-1)=(2.303)/(120s)"log"([R]_(0))/([R])` `"log"([R]_(0))/([R])=(5xx10^(-4)sxx120s)/(2.303)=0.02605 or ([R]_(0))/([R])=1.061` Substitutingthe value of `[R]_(0)`, we have `(0.25)/([R])=1.061 or [R]=(0.25)/(1.061)=0.23M` Half-life can be calcualted USING the relation: `t_(1//2)=(0.693)/(k)=(0.693)/(5xx10^(-4)s^(-1))=1386s`