Question

Uranyl nitrate decomposes according to UO2(NO3)2(aq) -> UO3(s) +2 NO 2 (g)+ 1/2 O2(g) The following data were recorded for the reaction at 25 °C t/min 20.0 60.0 180.0 360.0 [UO2(NOs)2]M 0.01413 0.01096 0.00758 0.00302 0.00055 Determine the order of reaction and rate constant for the reaction

Answer 1

Answer:

Given reaction is

UO2(NO3)2(aq) -----> UO3(s) + 2NO2(g) + 1/2O2(g)

Zero-order rate law is

[UO2(NO3)2]=-kt+[UO2(NO3)2]0 and the plot of [UO2(NO3)2] vs t gives a straight line with slope=-k.

The first-order rate law is

ln[UO2(NO3)2]=-kt+ln[UO2(NO3)2]0 and the plot of ln[UO2(NO3)2] vs t gives a straight line with slope=-k.

The second-order rate law is

1/[UO2(NO3)2]=kt+1/[UO2(NO3)2]0 and the plot of 1/[UO2(NO3)2] vs t gives a straight line with slope=k.

Where k=rate constant, [UO2(NO3)2]0=Initial concentration at t=0 min

[UO2(NO3)2]=concentration of UO2(NO3)2 at time t.

The calculated values are tabulated below

Time(s)	[UO2(NO3)2] (M)	ln[UO2(NO3)2]	1/[UO2(NO3)2]
0	1.41E-02	-4.259455082	70.77140835
20	1.10E-02	-4.513502997	91.24087591
60	7.58E-03	-4.882242079	131.9261214
180	3.02E-03	-5.802498448	331.1258278
360	5.50E-04	-7.50559228	1818.181818

[UO2(NO3)2] vs t plot is

0.016 0.014 y = a + b^x No Weighting 1.76722E-5 Equation Weight Residual Sum of Squares Pearson's r. Adj. R-Square 0.012 -0.926 0.80996 B Intercept Slope Value 0.01153 -3.45395E-5 Standard Error 0.00148 8.13012E-6 (w) ["on) onl 0.002 0.000 -50 0 50 100 250 300 350 400 150 200 Time (min)

ln[UO2(NO3)2] vs t plot is

1/[UO2(NO3)2] vs t plot is

y = a + b*x No Weighting 0.01399 o Equation Weight Residual Sum of Squares Pearson's r Adj. R-Square -0.99899 0.99732 o Intercept Slope Value -4.29873 -0.00882 Standard Error 0.04169 2.28785E-4 o Plon)'ondul o -8.0 + -50 0 50 100 250 300 350 400 150 200 Time (min)

2000 1800 - Equation y = a + b*x Weight No Weighting Residual Sum 264186.0743 of Squares Pearson's r. 0.93952 Adj. R-Squar 0.8436 Value Intercept -97.0197 Slope 4.72314 Standard Erro 181.12391 0.99405 Plon) onl/ -50 0 50 100 250 300 350 400 150 200 Time (min)

From the above plots, the plot of ln[UO2(NO3)2] vs t gives a straight line with R²=0.997.

Therefore the order of the reaction is first order.

The slope of the line=-k=-0.00882 min^-1

Therefore rate constant, k=0.00882 min^-1.