Step 1. Calculate the moles at #t = 0# and #t = "1 min"#.
At #t = 0#,
#"Moles of NO"_2 = 2.179 color(red)(cancel(color(black)("g NO"_2))) × ("1 mol NO"_2)/(46.01 color(red)(cancel(color(black)("g NO"_2)))) = "0.047 359 mol NO"_2#
At #t = "1 min"#,
#"Moles of NO"_2 = 1.879 color(red)(cancel(color(black)("g NO"_2))) × ("1 mol NO"_2)/(46.01 color(red)(cancel(color(black)("g NO"_2)))) = "0.040 839 mol NO"_2#
Step 2. Calculate the concentrations at #t = 0# and #t = 1 min#.
At #t = 0#,
#["NO"_2] = "0.047 359 mol"/"0.300 L" = "0.1579 mol/L"#
At #t = "1 min"#,
#["NO"_2] = "0.040 839 mol"/"0.300 L "= "0.1361 mol/L"#
Step 3. Calculate the average rate.
For the reaction
#"2NO"_2 → "2NO" + "O"_2#
the rate of reaction is defined as
#"rate" = -1/2(Δ["NO"_2])/(Δt)#
#(Δ["NO"_2])/(Δt) = (["NO"_2]_2 - ["NO"_2]_1)/(t_2 - t_1) = "0.1361 mol/L - 0.1579 mol/L"/"1 min - 0" = "-0.0218 mol·L"^"-1""min"^"-1"#
∴ #"rate" = -1/2("-0.0218 mol·L"^"-1""min"^"-1") = "0.0109 mol·L"^"-1"color(red)(cancel(color(black)("min"^"-1"))) × (1 color(red)(cancel(color(black)("min"))))/"60 s"#
#= 1.82 × 10^"-4" color(white)(l)"mol·L"^"-1""s"^"-1"#
