Chemistry College

The next two questions provide some more practice on calculations using half-lives. The isotope 64Cu has t1/2 of 12.7 hours. If the initial concentration of this isotope in an aqueous solution is 845 ppm, what will the abundance be after 4.00 hours? To solve this problem, first use equation (7) to determine k for 64Cu; then use this k value in equation (6) to obtain the amount of 64Cu, A, remaining after 4.00 hours if the amount present at the start, A0, is 845 ppm.

Answers

Answer 1

Answer:

The value is [tex] A = 679.5 \ ppm[/tex]

Explanation:

From the question we are told that

The half life of [tex]^{64}Cu[/tex] is [tex] t_h = 12.7 \ hr [/tex]

   The  initial concentration is   [tex] A_o  = 845 \  ppm [/tex]

    The time duration is   [tex] t =  4 \  hr  [/tex]

     

Generally the rate constant is mathematically represented as

       [tex] k =  \frac{0.693}{t_h} [/tex]

        [tex] k =  \frac{0.693}{12.7} [/tex]

       [tex] k = 0.0545 \  hr^{-1} [/tex]

This rate constant is also mathematically represented as

           [tex] k =  \frac{1}{t} *  ln (\frac{A_o}{A}) [/tex]

Here  A is the remaining concentration after t

So

             [tex]  0.0545 =  \frac{1}{4} *  ln (\frac{845}{A}) [/tex]

             [tex] 0.218 =  ln (\frac{845}{A}) [/tex]

             [tex] e^{0.218} =   \frac{845}{A} [/tex]

              [tex] 1.2436 =   \frac{845}{A} [/tex]

             [tex] A =   \frac{845}{1.2436} [/tex]

             [tex] A =   679.5 \  ppm[/tex]

Related Questions

The Ka values for several weak acids are given below. Which acid (and its conjugate base) would be the best buffer at pH 3.7?a. MES: Ka 7.9 x 10b. HEPES; Ka 3.2 x 103c. Tris; Ka 6.3 x 109d. Formic acid: K 1.8 x 10
e. Acetic acid: K 1.8 x 10

Answers

Answer:

Formic acid and Acetic acid is the best buffer at pH 3.7.

Explanation:

Given that,

The Ka values for several weak acids are given,

[tex]K_{a}\ of\ MES=7.9\times10^{-7}[/tex]

[tex]K_{a}\ of\ HEPES = 3.2\times10^{-3}[/tex]

[tex]K_{a}\ of\ Tris=6.3\times10^{-9}[/tex]

[tex]K_{a}\ of\ formic\ acid = 1.8\times10^{-4}[/tex]

[tex]K_{a}\ of\ Acetic\ acid = 1.8\times10^{-5}[/tex]

We need to calculate the pH of the weak acids with their [tex]pK_{a}[/tex] values

Using formula of [tex]pK_{a}[/tex]

For MES,

[tex]pK_{a}=-log K_{a}[/tex]

Put the value into the formula

[tex]pK_{a}=-log(7.9\times10^{-7})[/tex]

[tex]pK_{a}=7.0-log7.9[/tex]

[tex]pK_{a}=6.1[/tex]

pH range for best buffer,

[tex]pH=pK_{a}\pm 1[/tex]

Put the value into the formula

[tex]pH=6.1\pm 1[/tex]

[tex]pH=7.1, 5.1[/tex]

The pH value of the solution between 7.1 to 5.1.

This is not best buffer.

For HEPES,

[tex]pK_{a}=-log K_{a}[/tex]

Put the value into the formula

[tex]pK_{a}=-log(3.2\times10^{-3})[/tex]

[tex]pK_{a}=3.0-log3.2[/tex]

[tex]pK_{a}=2.5[/tex]

pH range for best buffer,

[tex]pH=pK_{a}\pm 1[/tex]

Put the value into the formula

[tex]pH=2.5\pm 1[/tex]

[tex]pH=3.5, 1.5[/tex]

The pH value of the solution between 3.5 to 1.5.

This is not best buffer.

For Tris,

[tex]pK_{a}=-log K_{a}[/tex]

Put the value into the formula

[tex]pK_{a}=-log(6.3\times10^{-9})[/tex]

[tex]pK_{a}=9.0-log6.3[/tex]

[tex]pK_{a}=8.2[/tex]

pH range for best buffer,

[tex]pH=pK_{a}\pm 1[/tex]

Put the value into the formula

[tex]pH=8.2\pm 1[/tex]

[tex]pH=9.2, 7.2[/tex]

The pH value of the solution between 9.2 to 7.2.

This is not best buffer.

For formic acid,

[tex]pK_{a}=-log K_{a}[/tex]

Put the value into the formula

[tex]pK_{a}=-log(1.8\times10^{-4})[/tex]

[tex]pK_{a}=4.0-log1.8[/tex]

[tex]pK_{a}=3.7[/tex]

pH range for best buffer,

[tex]pH=pK_{a}\pm 1[/tex]

Put the value into the formula

[tex]pH=3.7\pm 1[/tex]

[tex]pH=4.7, 2.7[/tex]

The pH value of the solution between 4.7 to 2.7.

This is best buffer.

For acetic acid,

[tex]pK_{a}=-log K_{a}[/tex]

Put the value into the formula

[tex]pK_{a}=-log(1.8\times10^{-5})[/tex]

[tex]pK_{a}=5.0-log1.8[/tex]

[tex]pK_{a}=4.7[/tex]

pH range for best buffer,

[tex]pH=pK_{a}\pm 1[/tex]

Put the value into the formula

[tex]pH=4.7\pm 1[/tex]

[tex]pH=5.7, 3.7[/tex]

The pH value of the solution between 5.7 to 3.7.

This is  best buffer

Hence, Formic acid and Acetic acid is the best buffer at pH 3.7.

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