# Environmental Health: Logarithms and Arsenic Levels

## Questions:

Earlier this year an alarm was raised on the Sunshine Coast of British Columbia when some wells showed arsenic levels in excess of the safe standard of 0.025 ppm. When testing a well a public health inspector would become suspicious of too high an arsenic level if the pH > 9.5.

1. If the hydrogen ion concentration in a specific well was 1.25x10-11, should the inspector be suspicious of too high an arsenic content ?
2. If a three litre sample of water contained 1 mg of arsenic, is the well safe?
3. What would the hydrogen ion concentration have to be to exactly meet the suspicious pH level ?

## Solution:

### Formula needed:

pH = - log [H + ]

### Conversion Facts Needed:

1 kg of water occupies approximately 1 litre

1 ppm (part per million) = 1 mg/kg

1. Find the pH of the water in the well:

pH = - log [H + ] = - log (1.25x10-11) =10.9

Since 10.9 > 9.5, yes, the inspector should be suspicious.

2. Find the concentration of arsenic:

3 liters = 3kg of water (for trace arsenic)

1mg of arsenic / 3kg of water = 0.33 ppm > 0.025 ppm

The well is not safe.

3. Find the concentration:

9.5 = - log [H + ]

- 9.5 = log [H + ]

10-9.5 = 3.162 x 10-10 = 3.16 x 10-10 concentration of = [H + ].

Written by Louise Routledge, Tuesday, June 24, 1997