How do I solve for a and b using the Van Der Waals equation using only the given values: P= 1 atm, V= 1.310 L, and T= 160 K

Answers

Answer 1

Answer:

[tex]a = \frac{24.79078- 1.7161b}{1.310 - b}[/tex]

[tex]b = 1.310 - \frac{22.5427}{a - 1.7161}[/tex]

Explanation:

Given

[tex]P = 1\ atm[/tex]

[tex]V = 1.310\ L[/tex]

[tex]T =160\ K[/tex]

Required

Solve for a and b

Van Der Waals equation is:

[tex]P = \frac{RT}{V - b} - \frac{a}{V^2}[/tex]

Substitute values for P, V and T, we have:

[tex]1 = \frac{R*160}{1.310 - b} - \frac{a}{1.310^2}[/tex]

R is a constant and the value is:

[tex]R = 0.0821[/tex]

So, the equation becomes:

[tex]1 = \frac{0.0821*160}{1.310 - b} - \frac{a}{1.310^2}[/tex]

Simplify the expression

[tex]1 = \frac{13.136}{1.310 - b} - \frac{a}{1.7161}[/tex] ----- (a)

Solving for (a):

[tex]1 + \frac{13.136}{1.310 - b} = \frac{a}{1.7161}[/tex]

Multiply both sides by 1.7161

[tex]a = [1 + \frac{13.136}{1.310 - b}] * 1.7161[/tex]

Take LCM

[tex]a = [\frac{1.310 - b+13.136}{1.310 - b}] * 1.7161[/tex]

Evaluate like terms

[tex]a = [\frac{14.446- b}{1.310 - b}] * 1.7161[/tex]

Open bracket

[tex]a = [\frac{24.79078- 1.7161b}{1.310 - b}[/tex]

Solving for (b), we have:

[tex]1 + \frac{13.136}{1.310 - b} = \frac{a}{1.7161}[/tex]

Subtract 1 from both sides

[tex]\frac{13.136}{1.310 - b} = \frac{a}{1.7161}-1[/tex]

Take LCM

[tex]\frac{13.136}{1.310 - b} = \frac{a-1.7161}{1.7161}[/tex]

Inverse both sides

[tex]\frac{1.310 - b}{13.136} = \frac{1.7161}{a - 1.7161}[/tex]

Multiply both sides by 13.136

[tex]1.310 - b = 13.136 * \frac{1.7161}{a - 1.7161}[/tex]

[tex]1.310 - b = \frac{22.5427}{a - 1.7161}[/tex]

Collect like terms

[tex]b = 1.310 - \frac{22.5427}{a - 1.7161}[/tex]


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Answers

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˚*・༓☾✧.* ☽༓・*˚⁺‧

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