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CHEM112 CHAP 14 Mastering Chemistry
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Key Concepts:
Terms in this set (42)
In a reaction involving reactants in the gas state, how does increasing the partial pressures of the gases affect the reaction rate?
The rate will increase.
How does the instantaneous rate of reaction change as the reaction proceeds?
It decreases.
An average reaction rate is calculated as the change in the concentration of reactants or products over a period of time in the course of the reaction. An instantaneous reaction rate is the rate at a particular moment in the reaction and is usually determined graphically.
The reaction of compound A forming compound B was studied and the following data were collected:
Time (s) [A] (M)
0. 0.184
200. 0.129
500. 0.069
800. 0.031
1200. 0.019
1500. 0.016
What is the average reaction rate between 0. and 1500. s?
Express your answer to three significant figures and include the appropriate units.
rate = 1.12×10^(−4) M/s
What is the average reaction rate between 200. and 1200.s ?
Express your answer to three significant figures and include the appropriate units.
rate = 1.10×10^(−4) M/s
What is the instantaneous rate of the reaction at t=800. s?
Express your answer to two significant figures and include the appropriate units.
rate =
6.8⋅10^(−5) M/s
Learning Goal:
To calculate average and relative reaction rates.
You can measure the rate of a reaction, just like you can measure the speed a jogger runs. While a jogger would be reported to run a specific number of miles in an hour, miles/hour, a reaction is reported to form product or consume reagent in molar concentration per second, M/s.
Reaction rate can be defined either as the increase in the concentration of a product per unit time or as the decrease of the concentration of a reactant per unit time. By definition, reaction rate is a positive quantity.
In the reaction X→2Y, for example, Y is being produced twice as fast as X is consumed and thus
rate of X=12(rate of Y)
Each rate can be expressed as the change in concentration over the change in time, Δt:
−Δ[X]Δt=12(Δ[Y]Δt)
Consider the reaction
2H3PO4→P2O5+3H2O
Using the information in the following table, calculate the average rate of formation of P2O5 between 10.0 and 40.0 s.
Time (s) 0 10.0 20.0 30.0 40.0 50.0
[P2O5] (M) 0 1.40×10−3 4.40×10−3 6.20×10−3 7.40×10−3 8.00×10−3
Express your answer with the appropriate units.
Rate of formation of P2O5 = 2.00×10^(−4) M/s
Determine the average rate of decomposition of H3PO4 between 10.0 and 40.0 s.
Express your answer with the appropriate units.
Rate of decomposition of H3PO4 = −4.00×10^(−4) M/s
Consider the reaction
5Br−(aq)+BrO−3(aq)+6H+(aq)→3Br2(aq)+3H2O(l)
The average rate of consumption of Br− is 1.66×10−4M/s over the first two minutes. What is the average rate of formation of Br2 during the same time interval?
Express your answer with the appropriate units.
Rate of formation of Br2Br2 = 9.96×10^(-5) M/s
What is the average rate of consumption of H+ during the same time interval?
Express your answer with the appropriate units.
Rate of consumption of H+ = −1.99×10^(−4) Ms
Imagine that you took a road trip. Based on the information in the table, what was the average speed of your car?
Time Mile marker
3:00 pm 40
8:00 pm 290
Express your answer to three significant figures and include the appropriate units.
50 mph
Now consider the following reaction and data:
H2+2BrCl→2HCl+Br2
Time
(s) Br2 concentration (M)
5 1.5
15 1.57
Part B
What is the average rate of formation of Br2?
Express your answer to three decimal places and include the appropriate units.
0.007 M/s
Based on your answer to Part B, what is the average rate of formation of HCl?
Express your answer to three decimal places and include the appropriate units.
0.014 M/s
Based on your answer to Part B or C, what is the average rate of change of H2? Remember that reactant concentrations decrease over time.
Express your answer to three decimal places and include the appropriate units.
0.007 M/s
Rate law equation
The rate of a chemical reaction depends on the concentrations of the reactants. For the general reaction between Aand B,
aA+bB⇌cC+dD
The dependence of the reaction rate on the concentration of each reactant is given by the equation called the rate law:
rate=k[A]m[B]n
where k is a proportionality constant called the rate constant. The exponent m determines the reaction order with respect to A, and n determines the reaction order with respect to B. The overall reaction order equals the sum of the exponents (m+n).
What is the reaction order with respect to A?
Express your answer as an integer.
2
What is the reaction order with respect to B?
Express your answer as an integer.
0
What is the reaction order with respect to C?
Express your answer as an integer.
1
What is the value of the rate constant k for this reaction?
Express your answer to two significant figures and include the appropriate units. Indicate the multiplication of units explicitly either with a multiplication dot or a dash.
k = 1.9×10^(−3) M^(−2)⋅s^(−1)
Given the data calculated in Parts A, B, C, and D, determine the initial rate for a reaction that starts with 0.55M of reagent A and 0.70M of reagents B and C?
Express your answer to two significant figures and include the appropriate units. Indicate the multiplication of units explicitly either with a multiplication dot or a dash.
4.0×10^(−4) M/s
Calculate the initial rate for the formation of C at 25 ∘C, if [A]=0.50M and [B]=0.075M.
Express your answer to two significant figures and include the appropriate units.
initial rate = 2.3×10^(−2) M/s
Consider the reaction of ethyl bromide with sodium hydroxide:
CH3CH2Br(aq)+NaOH(aq)⇌CH3CH2OH(aq)+NaBr(aq)
The reaction is first order in NaOH and second order overall. What is the rate law?
rate=k[CH3CH2Br][NaOH]
The reaction of ethyl bromide with sodium hydroxide,
CH3CH2Br(aq)+NaOH(aq)⇌CH3CH2OH(aq)+NaBr(aq)
is first order in CH3CH2Br and first order in NaOH. If the concentration of CH3CH2Br was increased by half and the concentration of NaOH was quadrupled, by what factor would the reaction rate increase?
Express your answer numerically.
6
Analyzing a specific reaction
Consider the following reaction:
2Mg+O2→2MgO,rate=k[Mg][O2]2
Part A
What is the overall reaction order?
Express your answer as an integer.
3
What are the units of the rate constant k for this reaction?
M^(−2)⋅s^(−1)
What would happen to the rate if [Mg] were doubled?
double
What would happen to the rate if [O2] were doubled?
quadruple
What can you conclude from the fact that the plot of ln p versus t is linear?
The reaction is first order in CH3NC
How does the half-life of a second-order reaction change as the reaction proceeds?
The half-life will increase.
There are six different reactions you can access in the simulation using the drop-down menu. Which of the following are second-order reactions?
Check all that apply.
2HI→H2+I2
2NO2→2NO+O2
Consider the following mechanism:
Step 1 (fast): 2 A → B
Step 2 (slow): B + 2 C → D + E
Step 3 (fast): D + C → E + F
Choose the correct statement.
The rate-determining step is termolecular.
What is the molecularity of the elementary reaction?
NO(g)+Cl2(g)→NOCl(g)+Cl(g)
bimolecular
How do the two graphs compare if the activation energy of the second reaction is higher than the activation energy of the first reaction but the two reactions have the same frequency factor?
The lines will have the same y-intercept, negative slope direction, and the slope of line 2 will be steeper than the slope of line 1.
How do the two graphs compare if the frequency factor of the second reaction is higher than the frequency factor of the first reaction but the two reactions have the same activation energy?
The lines will have the same negative slope, and the y-intercept of line 2 will be higher than the y-intercept of line 1.
According to the Arrhenius equation:
the rate constant increases as E a decreases.
Consider the second-order reaction:
2HI(g)→H2(g)+I2(g)
Use the simulation to find the initial concentration [HI]0 and the rate constant k for the reaction. What will be the concentration of HI after t = 8.87×1010s ([HI]t) for a reaction starting under the condition in the simulation?
Express your answer in moles per liters to three significant figures.
[HI]t = 1.8×10^(−3) mol/L
Consider a second-order reaction in which reactant A decomposes according to the chemical equation 2A→products.
The data given below is the time, in minutes, and the corresponding change in the concentration of reactant A for this reaction.
t (min) [A]t(M)
0.00 0.500
20.0 0.382
40.0 0.310
60.0 0.260
80.0 0.224
Part C
For a second-order reaction, the rate constant k is the slope of the graph of 1[A] versus t. Based on this information and the data given, calculate the rate constant k for the reaction.
Express your answer in M−1⋅min−1 to three significant figures.
The rate constant k = 3.10×10^(−2) M−1⋅min−1
A catalyst speeds up the rate of a chemical reaction by:
using a mechanism with lower activation energy.
Based on the data given and a rate constant of 0.031 M−1⋅min−1, calculate the time at which the concentration of reactant A will be 0.125M .
Express your answer in minutes to two significant figures.
t = 190 min
Using the integrated rate law for a second-order reaction, the time at which the concentration of reactant A will be 0.125M can be calculated as
t===(1[A]t−1[A]0)/k(10.125M−10.500 M)/0.031 M−1⋅min−1194 min
Suppose that a certain biologically important reaction is quite slow at physiological temperature (37 ∘C) in the absence of a catalyst.
Assuming that the collision factor remains the same, by how much must an enzyme lower the activation energy of the reaction in order to achieve a 3×105-fold increase in the reaction rate?
Express your answer using one significant figure.
Eauncatalized−Eacatalized = 30 kJ/mol
The integrated rate laws for zero-, first-, and second-order reaction may be arranged such that they resemble the equation for a straight line,y=mx+b.
Order Integrated Rate Law Graph Slope
0 [A]=−kt+[A]0 [A] vs. t −k
1 ln[A]=−kt+ln[A]0 ln[A] vs. t −k
2 1[A]= kt+1[A]0 1[A] vs. t k
The reactant concentration in a zero-order reaction was 5.00×10−2M after 175s and 4.00×10−2M after 305s . What is the rate constant for this reaction?
Express your answer with the appropriate units.
k0th =
7.69×10^−5 M/s
What was the initial reactant concentration for the reaction described in Part A?
Express your answer with the appropriate units.
[A]0 = 6.35×10^−2 M
The reactant concentration in a first-order reaction was 9.20×10−2M after 30.0s and 7.80×10−3M after 85.0s . What is the rate constant for this reaction?
Express your answer with the appropriate units.
k1st = 4.49×10^−2 s−1
The reactant concentration in a second-order reaction was 0.620M after 220s and 7.50×10−2M after 875s . What is the rate constant for this reaction?
Express your answer with the appropriate units. Include an asterisk to indicate a compound unit with mulitplication, for example write a Newton-meter as N*m.
k2nd = 1.79×10^−2 M^−1⋅s^−1
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