The isomerization of methyl isonitrile (CH 3 NC) to acetonitrile (CH 3 CN) was studied in the gas phase at 215°C, and the following data were obtained: Time (s) [CH 3 NC] (M) 0 0.0165 2000 0.0110 5000 0.00591 8000 0.00314 12,000 0.00137 15,000 0.00074 (d) Graph [CH 3 NC] versus time and determine the instantaneous rates in M/s at t = 5000 s and t = 8000 s.

Hey everyone today, we're being given the data for the purification of acetic acid with ethanol and were given the specifically concentration of acetic acid. As time progresses. Given this data, we're asked to plot a graph and calculate the instantaneous rate of the reaction at times 10,000 seconds. And when time is at 25,000 seconds. Now, I've gone ahead and brought in the plotted values. And a very important thing to note is that to find the instantaneous rate of reaction, especially when given a curve like this, we need to find the slope of the tangent line at that specific point on the curve. So let's go ahead and draw the tension line for the 10,000 seconds first. And this isn't exact but it'll look something like this. No. Now, while that's not perfect, I'd say that's pretty close to what we need but to find the slope, since we don't really have a Y intercept and we're dealing with a curve, not a linear line. In this case, we can actually use a variation of the point slope form in order to find the slope X 2 -11. And we'll go ahead and label our smaller values as one in like X one and Y one and our larger ones at X two and Y two. And you'll see what I mean in just a second. So right here why one is equal to 0. and why to Which will be right about here, let's say why two will be equal to 0.6. Similarly, X one will be 5000 And X two will equal 10, plugging this into the formula. Right over here we get that 0.6 -0. divided by 10, -5000. Once simplified Gives us a final value of 4. times 10 to the negative 5th Mueller per second. So this is the instantaneous rate of the reaction. When time is 10,000 seconds we can use a similar process for When time is at 25,000 seconds. Let me go ahead and draw out the tangent line at that point and we'll draw this in red for a little variation. I'd say that's pretty close. So anyways, using the same conventions we can go ahead and find D X one, Y one and X two and Y two for these values. So let's say why one is equal to 0.1 here and why two is about 0.14. Uh X one is equal to 20,000 And X two. musical to 25,000. Plugging this back into the formula will get that M is equal to excuse me, M is equal to 0.14 -0.1 divided by 25, -20000 Which gives us a final answer of 8.0 times 10 to the - Mueller per second. And that is the instantaneous rate of the reaction at time Is equal to 25, seconds and this is Ed T is equal to 10,000 seconds. I hope this helps, and I look forward to seeing you all in the next one.

Ch.14 - Chemical Kinetics

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Brown 14th Edition

Ch.14 - Chemical Kinetics

Problem 21d

Chapter 14, Problem 21d

The isomerization of methyl isonitrile (CH₃NC) to acetonitrile (CH₃CN) was studied in the gas phase at 215°C, and the following data were obtained:
Time (s) [CH₃NC] (M)
0 0.0165
2000 0.0110
5000 0.00591
8000 0.00314
12,000 0.00137
15,000 0.00074
(d) Graph [CH₃NC] versus time and determine the instantaneous rates in M/s at t = 5000 s and t = 8000 s.

Verified step by step guidance

Step 1: Start by plotting the concentration of CH3NC (y-axis) against time (x-axis). You can use any graphing tool or software to do this. The concentration of CH3NC should decrease over time as it is converted to CH3CN.

Step 2: To find the instantaneous rate at a specific time, you need to determine the slope of the tangent line to the curve at that point. This represents the rate of change of concentration at that specific time.

Step 3: To find the instantaneous rate at t = 5000 s, draw a tangent line to the curve at t = 5000 s and calculate its slope. The slope of the tangent line is equal to the change in concentration divided by the change in time (Δ[CH3NC]/Δt).

Step 4: Repeat the process for t = 8000 s. Draw a tangent line to the curve at t = 8000 s and calculate its slope. This will give you the instantaneous rate at t = 8000 s.

Step 5: Remember that the instantaneous rate of a reaction at a particular time is the slope of the tangent to the curve of concentration versus time at that time. It represents the speed of the reaction at that specific moment.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Isomerization

Isomerization is a chemical process where a compound is transformed into one of its isomers, which are molecules with the same molecular formula but different structural arrangements. In this case, methyl isonitrile is converted to acetonitrile, highlighting the importance of understanding structural differences and their implications on chemical properties and reactivity.

Reaction Rate

The reaction rate refers to the speed at which reactants are converted into products in a chemical reaction. It can be expressed in terms of concentration change over time, typically in units of molarity per second (M/s). Understanding how to calculate and interpret reaction rates is crucial for analyzing kinetic data, such as the provided concentration values over time.

Graphical Analysis of Kinetics

Graphical analysis in kinetics involves plotting concentration versus time to visualize the reaction's progress and determine instantaneous rates. By analyzing the slope of the concentration-time graph at specific time points, such as 5000 s and 8000 s, one can derive the rate of reaction at those moments, which is essential for understanding the dynamics of the isomerization process.

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Textbook Question

A flask is charged with 0.100 mol of A and allowed to react to form B according to the hypothetical gas-phase reaction A1g2¡B1g2. The following data are collected: Time (s) 0 40 80 120 160 Moles of A 0.100 0.067 0.045 0.030 0.020 (c) Which of the following would be needed to calculate the rate in units of concentration per time: (i) the pressure of the gas at each time, (ii) the volume of the reaction flask, (iii) the temperature, or (iv) the molecular weight of A?

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Textbook Question

The isomerization of methyl isonitrile (CH₃NC) to acetonitrile (CH₃CN) was studied in the gas phase at 215°C, and the following data were obtained:

Time (s) [CH₃NC] (M)

0 0.0165

2000 0.0110

5000 0.00591

8000 0.00314

12,000 0.00137

15,000 0.00074

(a) Calculate the average rate of reaction, in M/s, for the time interval between each measurement. (c) Which is greater, the average rate between t = 2000 and t = 12,000 s, or between t = 8000 and t = 15,000 s?

Textbook Question

The isomerization of methyl isonitrile (CH₃NC) to acetonitrile (CH₃CN) was studied in the gas phase at 215°C, and the following data were obtained:

Time (s) [CH₃NC] (M)

0 0.0165

2000 0.0110

5000 0.00591

8000 0.00314

12,000 0.00137

15,000 0.00074

(b) Calculate the average rate of reaction over the entire time of the data from t = 0 to t = 15,000 s.

560

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Textbook Question

The rate of disappearance of HCl was measured for the following reaction: CH3OH1aq2 + HCl1aq2¡CH3Cl1aq2 + H2O1l2 The following data were collected: Time (min) 3HCl 4 1M2 0.0 1.85 54.0 1.58 107.0 1.36 215.0 1.02 430.0 0.580 (a) Calculate the average rate of reaction, in M>s, for the time interval between each measurement.

553

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Textbook Question

The rate of disappearance of HCl was measured for the following reaction: CH3OH1aq2 + HCl1aq2¡CH3Cl1aq2 + H2O1l2 The following data were collected: Time (min) 3HCl 4 1M2 0.0 1.85 54.0 1.58 107.0 1.36 215.0 1.02 430.0 0.580 (b) Calculate the average rate of reaction for the entire time for the data from t = 0.0 min to t = 430.0 min.

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Textbook Question

The rate of disappearance of HCl was measured for the following reaction: CH3OH1aq2 + HCl1aq2¡CH3Cl1aq2 + H2O1l2 The following data were collected: Time (min) 3HCl 4 1M2 0.0 1.85 54.0 1.58 107.0 1.36 215.0 1.02 430.0 0.580 (c) Which is greater, the average rate between t = 54.0 and t = 215.0 min, or between t = 107.0 and t = 430.0 min?

360

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