Quick physical chemistry question

In summary, The final temperature of a sample of carbon dioxide can be calculated by using the equation Tf = Ti (Vi/Vf)^(1/c). The value of c can be found by using the equation c = Cv,m/R, which in this case is 3.463. However, some additional information may be needed to make the calculation, such as the value of Cv,m or R, which can be found in the back of the book.
  • #1
gman5
2
0
Calculate the final temperature of a sample of carbon dioxide of mass 16.0g that is
expanded reversibly and adiabatically from 500mL at 298,15K to 2.00L.

I know the answer and understand how to do the problem except for 1 part.

The equation to get the solution is : Tf = Ti (Vi/Vf)^(1/c)

The part I cannot figure out is how to find c. I know c = Cv,m/R = 3.463, but when I try to calculate c I get something other than 3.463.
 
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  • #2
nevermind, it turns out that some information needed to make the calculation is contained in the back of the book, so I figured it out.
 
  • #3


Hello,

Thank you for your question. To calculate the final temperature of the sample of carbon dioxide, we will need to use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.

In this case, we know the initial conditions (500mL at 298.15K) and the final volume (2.00L). We also know that the process is adiabatic, meaning there is no heat transfer, so Q = 0. This means that the change in internal energy (ΔU) is equal to the work done on the gas (W). We can use the first law of thermodynamics, ΔU = Q - W, to solve for W.

W = -PΔV = -P(Vf - Vi) = -P(Vf/Vi - 1)

We can then substitute this into the ideal gas law to get:

ΔU = nRTf - nRTi = 0 - (-P(Vf/Vi - 1)) = P(Vf/Vi - 1)

Solving for Tf, we get:

Tf = Ti - (P(Vf/Vi - 1))/(nR)

To find c, we can use the specific heat capacity at constant volume (Cv) for carbon dioxide, which is 0.655 J/mol*K. However, we need to convert this to specific heat capacity at constant pressure (Cp) using the relationship Cp = Cv + R.

Cp = 0.655 J/mol*K + 8.314 J/mol*K = 8.969 J/mol*K

Now, we can use the relation c = Cv,m/R to find c:

c = 8.969 J/mol*K / 8.314 J/mol*K = 1.08

Substituting this into the equation for Tf, we get:

Tf = 298.15K - (P(Vf/Vi - 1))/(n*1.08)

Finally, we can use the ideal gas law to calculate the pressure (P) and number of moles (n) of carbon dioxide:

P = nRT/V = (16.0g/44.01g/mol)(8.314 J/mol*K)(298.15K)/(500mL)(1L/
 

What is physical chemistry?

Physical chemistry is a branch of chemistry that focuses on the study of the physical properties and behavior of matter. It combines principles from physics and chemistry to study the structure, composition, and change of matter at a molecular and atomic level.

What is the difference between physical and chemical properties?

Physical properties are characteristics of a substance that can be observed or measured without changing its chemical composition. Examples include color, density, and melting point. Chemical properties, on the other hand, describe a substance's ability to undergo a chemical change. These properties can only be observed through a chemical reaction.

What are some common applications of physical chemistry?

Physical chemistry has a wide range of applications in various fields, including materials science, environmental science, and pharmaceuticals. It is used to study and develop new materials with specific properties, understand atmospheric and oceanic processes, and design and optimize drug molecules.

What is the relationship between thermodynamics and physical chemistry?

Thermodynamics is a subfield of physical chemistry that deals with the study of energy and its transformations in chemical systems. It helps to understand and predict the behavior of chemical reactions and the changes in energy that occur during these reactions.

How is physical chemistry related to other branches of chemistry?

Physical chemistry is closely related to other branches of chemistry such as organic chemistry, inorganic chemistry, and analytical chemistry. It provides a foundation for understanding the properties and behavior of chemical compounds, which is essential for these other branches to study and manipulate substances in different contexts.

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