r=[A]m[B]n APPLEX
To determine the rate of the reaction using the rate law ( \text{rate} = k[A]^m[B]^n ), we can substitute the values given. With ( k = 1.5 , \text{M}^{-2}\text{s}^{-1} ), ( [A] = 1 , \text{M} ), ( [B] = 3 , \text{M} ), ( m = 2 ), and ( n = 1 ), the rate can be calculated as follows: [ \text{rate} = 1.5 \times (1)^2 \times (3)^1 = 1.5 \times 1 \times 3 = 4.5 , \text{M/s} ] Thus, the rate of the reaction is ( 4.5 , \text{M/s} ).
To calculate the rate of a reaction, you typically use the rate law equation, which can be expressed as ( \text{Rate} = k[A]^m[B]^n ), where ( k ) is the rate constant, ( [A] ) and ( [B] ) are the concentrations of the reactants, and ( m ) and ( n ) are their respective orders. Assuming a simple first-order reaction with respect to both A and B (i.e., ( m = n = 1 )), the rate would be calculated as ( \text{Rate} = 0.1 \times (1)^1 \times (2)^1 = 0.2 , \text{M/s} ). Thus, the reaction rate is 0.2 M/s.
The Law of 4 Laws of addition and multiplication Commutative laws of addition and multiplication. Associative laws of addition and multiplication. Distributive law of multiplication over addition. Commutative law of addition: m + n = n + m . A sum isn't changed at rearrangement of its addends. Commutative law of multiplication: m · n = n · m . A product isn't changed at rearrangement of its factors. Associative law of addition: ( m + n ) + k = m + ( n + k ) = m + n + k . A sum doesn't depend on grouping of its addends. Associative law of multiplication: ( m · n ) · k = m · ( n · k ) = m · n · k . A product doesn't depend on grouping of its factors. Distributive law of multiplication over addition: ( m + n ) · k = m · k + n · k . This law expands the rules of operations with brackets (see the previous section).
The rate of a reaction can be expressed using the rate law equation, which typically takes the form ( \text{Rate} = k[A]^m[B]^n ), where ( k ) is the rate constant, and ( A ) and ( B ) are the concentrations of the reactants raised to their respective powers ( m ) and ( n ). In this case, if ( k = 3 ), ( [A] = 2 , \text{M} ), and ( [B] = 2 , \text{M} ), and assuming ( m ) and ( n ) are both 1 (first-order with respect to both reactants), the rate would be calculated as ( \text{Rate} = 3 \times (2)^1 \times (2)^1 = 3 \times 2 \times 2 = 12 , \text{M/s} ). If the orders of the reaction are different, the calculation would change accordingly.
Rate = k[A]m[B]n
They are experimentally determined exponents.
r=[A]m[B]n APPLEX
They are experimentally determined exponents
The general form of a rate law is rate = k[A]^m[B]^n, where rate is the reaction rate, k is the rate constant, [A] and [B] are the concentrations of reactants A and B, and m and n are the respective reaction orders for A and B.
To determine the rate of the reaction that follows the rate law rate = k[A]^m[B]^n, where k = 3 M^(-2) s^(-1), [A] = 2 M, and [B] = 3 M, we first need to substitute these values into the rate law. Given that m = 2 and n = 3, the rate can be calculated as follows: Rate = k[A]^m[B]^n = 3 M^(-2) s^(-1) * (2 M)^2 * (3 M)^3 = 3 * 4 * 27 = 324 M/s. Thus, the rate of the reaction is 324 M/s.
The equation is called the rate law equation. For the reaction aA+bB =>cC+dD the rate law would be rate = k[A]^m[B]^n where k is the rate constant and m and n are the "order" with respect to each reactant. m and n must be determined experimentally and may or may not be the same as the coefficients a and b.
In the rate law equation ( \text{rate} = k[A]^m[B]^n ), ( m ) and ( n ) represent the reaction orders with respect to the reactants ( A ) and ( B ), respectively. These values indicate how the reaction rate is affected by the concentrations of the reactants: ( m ) shows the sensitivity of the rate to changes in concentration of ( A ), while ( n ) does the same for ( B ). The orders are determined experimentally and can be whole numbers, fractions, or zero, depending on the reaction mechanism.
The rate of reaction that follows the rate law ( \text{Rate} = k [A]^m [B]^n ) indicates that the reaction rate depends on the concentrations of reactants ( A ) and ( B ), raised to their respective powers ( m ) and ( n ). The constant ( k ) is the rate constant, which is specific to the reaction at a given temperature. The values of ( m ) and ( n ) represent the order of the reaction with respect to each reactant, which can be determined experimentally. Overall, the overall order of the reaction is the sum ( m + n ).
r=[A]m[B]n APPLEX
The rate of the reaction can be calculated using the rate law rate = k[A]^m[B]^n. Plugging in the given values: rate = 0.02*(3)^3*(3)^3 = 0.022727 = 14.58 M/s.
5.4 (apex)