Solve Work Problem: 2.03 mol He, 295 K, 0.350 atm to 1.00 atm

In summary, the problem involves a 2.03 mol sample of helium gas being compressed isothermally from 295 K and 0.350 atm to 1.00 atm. The helium is assumed to behave as an ideal gas. The question is asking for the work done on the gas. The correct formula for work in this case is W = (nRT)ln(v_i/v_f), where n is the number of moles, R is the ideal gas constant, T is the temperature, and v_i and v_f are the initial and final volumes, respectively. There may be some errors in the calculations provided, as the correct answer is 7.03 kJ and the pressure used to calculate the work
  • #1
nemzy
125
0
here is the problem:

A 2.03 mol sample of helium gas initially at 295 K and 0.350 atm is compressed isothermally to 1.00 atm. Assume that the helium behaves as an ideal gas.


what is the work done on the gas.




well i know that w=-p*change in volume

i can figure out the final and initial volume using the ideal gas law pv=nrt at the initial and final pressures...so i know what the change in volumeis, but what would the pressure be when calculating the work? i used both 1 atm and .35 atm and i stil get the wrong answer...here is my work

final volume: pv=nrt
p=1.8 atm
n=2.18 mol
r= .0821 liters*atm/mol*k
t=305 k

final volume = .0303 m^3

initial volume: pv=nrt
p=.505 atm
n=2.18
r=.0821 liters*atm/mol*k
t=305 k

initial volume = .108 m^3

change in volume = .0778 m^3

work = -p(change in volume)


the answer is suppose to be 7.03 kj, which means that if my volume calculations were right, the pressure is suppose to be .893 atm?? does anyone know where i went wrong?
 
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  • #2
Work is defined as integral of pdv => w=Int{pdv}=Int{nRT(dv/v)},where t is constant bacause the process is isothermic => w=(nRT)In{(v_f)/(v_i)} and
v_f/v_i = p_i/p_f.
There are some other problems like"A 2.03 mol sample..." and then you used n=2.18 also "... at 295 K..." T= 305k... and so on
 
  • #3
incorrect on the W there...W=(nrt)ln(v_i/v_f)...
 

1. What is the formula for solving this work problem?

The formula for solving this work problem is P1V1 = P2V2, where P1 and V1 represent the initial pressure and volume, and P2 and V2 represent the final pressure and volume.

2. How do you convert from moles to volume in this problem?

In order to convert from moles to volume, you can use the ideal gas law which states that V = nRT/P, where V is the volume, n is the number of moles, R is the gas constant, T is the temperature, and P is the pressure.

3. Can you explain the significance of the given temperature and pressure values?

The given temperature of 295 K and pressure of 0.350 atm represent the initial conditions of the gas before it is brought to its final pressure of 1.00 atm. These values are important in determining the change in volume of the gas.

4. What is the value of the gas constant (R) in this problem?

The gas constant (R) in this problem has a value of 0.0821 L·atm/mol·K. This value is a constant used in the ideal gas law to relate the properties of gases.

5. How do you solve for the final volume (V2) in this problem?

To solve for the final volume (V2), you can rearrange the ideal gas law to V2 = (nRT2)/P2, where n is the number of moles, R is the gas constant, T2 is the final temperature, and P2 is the final pressure.

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