A fishing boat reports an oil spill near a ship to the local maritime authority.

Question

A fishing boat reports an oil spill near a ship to the local maritime authority. The ship is radioed and asked whether oil was being discharged from its vessel. The captain reports that the ship has discharged only 10 liters of heavy fuel waste oil during a bilge pump-out which is mixed with 100 tonnes of sea water. Has the ship exceeded the legal limit of oil discharge of 15 parts per million (15 parts of oil to 1 million parts of water)? Assume oil and sea water have the same density for the calculation (but see the tables in the lab background information, above, for closer estimates).

Explanation / Answer

Let us solve this question ins steps:

The ship has discharged 10 Liters oil in 100 tons of salt water.

Since density is assumed to be same for water and oil, let us assume the density to be 1 unit.

We know that Mass = Density x Volume. So, we can convert volume of oil to mass.

Mass of oil in kg = 1 x 10 Liters = 10 kg of oil.

Note: We want to bring both oil and water in the same units so we have converted volume to mass for oil since water quantity is also denoted in terms of mass. If we wanted to, we could also change the mass of water to volume to bring them under the same units as that of oil.

At this point we know that 10 kg of oil is mixed with 100 tons of water

Converting tons to kg:

1 ton = 1000 kg. So there is 100 x 1000 kg of water = 105 kg of water.

If we divide the mass of oil to the mass of water we get = 10 kg / 105 kg.

The unit kilogram (kg) can be cancelled since it is present in both numerator and denominator.

Now we get 10/105. Since there is no unit, we can call this a part. This means that there are 10 parts of oil for every 105 parts of water.

We know that 1 million = 106. If we bring the denominator of the above equation to 106, we can convert it to parts per million. Therefore, we will multiply the above equation with 10 / 10.

This gives us 100 / 106 The solution tells us that there are 100 parts of oil per million parts of water. This is above the allowed limit of 15 parts of oil per million parts of water.

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