
The first-order rate constant for the decomposition of dimethyl ether:
is

Interpretation:
The pressure of the system is to be determined.
Concept introduction:
The ideal gas equation elaborates the physical properties of gases by relating the pressure, volume, temperature, and number of moles with each other with the help of four gas laws. This can be shown by:
Here,
The formula for conversion of temperature from degree Celsius to Kelvin is represented as:
Answer to Problem 113AP
Solution:
Explanation of Solution
Given information:
Rate constant,
Temperature,
Pressure,
Time,
The temperature is
The conversion of temperature from degree Celsius to Kelvin can be done by using the formula given below:
The standard form of an ideal gas equation is:
Rearrange the above equation for number of moles of hydrogen as follows:
Substitute,
According to the Arrhenius equation
The concentration of dimethyl ether after
Thus, after
After
There are three moles of product formed from each mole of dimethyl ether reacting. So, the concentration of products is:
Molarity is equal to the ratio of number of moles to the volume as follows:
The pressure of dimethyl ether after
Substitute
Substitute
The pressure of the system (dimethyl ether) is
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Chapter 14 Solutions
EBK CHEMISTRY
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