# 2A(g) + B(g) -> C(g). Rate = k[A]^2[B]. At the beginning of one trial of this reaction, [A] = 4.0 M and [B] = 1.0 M. The observed rate was 0.048 "mol"*"L"^(-1)*"s"^(-1). What is the value of the rate constant for this reaction closest to?

The value of the rate constant is $\text{0.030 L"^2"mol"^"-2""s"^"-1}$.
"rate" = k["A"]^2["B"]
$k = \text{rate"/(["A"]^2["B"]) = (0.048 color(red)(cancel(color(black)("mol·L"^"-1")))"s"^"-1")/(("4.0 mol·L"^"-1")^2 × 1.0 color(red)(cancel(color(black)("mol·L"^"-1")))) = "0.0030 L"^2"mol"^"-2""s"^"-1}$