9-19. Calculate the pH of water at 25°C and 75°C. The values for pKw at these temperatures are 13.99 and 12.70, respectively.

The values of the pH of water at 25 °C (pKw = 13.99) and 75 °C (pKw = 12.70) are 6.99 and 6.35, respectively.

The equation for water dissociation is the following:

2H₂O ⇄ H₃O⁺ + OH⁻

The dissociation constant of the above reaction is:

Since the solution has only water, the concentrations of H₃O⁺ and OH⁻ are equal, so:

  (1)

Now, the pH given by:

  (2)

So, by entering equation (1) into (2):

  (3)

The pKw is equal to:

  (4)

Now, entering eq (4) into (3):

  (5)  

1. For the temperature of 25°C we have:

Hence, the pH of water at 25 °C is 6.99.

2. For the temperature of 75°C we have:

Then, the pH of water at 75 °C is 6.35.

Therefore, the pH of water at 25 °C and 75 °C are 6.99 and 6.35, respectively.

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7.00; 6.35

Explanation:

1. At 25 °C

2H₂O ⇌ H₃O⁺ + OH⁻

pH = ½pKw = ½ × 13.99 = 7.00

2. At 75° C

pH = ½pKw = ½ × 12.70 = 6.35

the density of gold = 19.3 g/cm3

the relation between density and mass and volume is

density = mass / volume

given :

mass of gold = 13 g

density = 13g / volume = 19.3

volume = 13 /19.3 = 0.67 cm^3

thus volume of gold nugget = 0.67 cm^3