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NorwegianKid
A water holding tank measures 90 m long, 60 m wide, and 9 m deep. Traces of mercury have been found in the tank, with a concentration of 65 mg/L. What is the total mass of mercury in the tank? Answer in units of kg
Int this case, we know the length, depth, and width of the tank, which makes it possible to calculate the volume of tank=90*60*9=48600m^3. The concentration of Hg is also provided. However, be sure to convert the volume into Liters. Keep in mind that 10L=1m^3. So the volume of the tank is 4.86*10^5L. Multiply the concentration of the Hg with the volume in Liters, you will get the mass of Hg. Since the question is asking mass in kg, you have to convert the mass from mg to kg. FYI, 1kg=10^3g=10^6mg.
thats confusing still i dont get how you find the answer in units of kg
This is a problem concerning the conversion of different units. The best thing to do is to convert all the given values into the same form of units before carrying out the calculation (that is change litres to cubic metres, and milligrams to kilograms. So we are told the dimensions of the tank in meters, which means that when we work out the volume of the tank, we will a volume in units of cubic metres (m\(^3\)). However, we are given the concentration in units of Litres. So first up we need to convert litres to cubic meters. We recall that there are 1000 cubic centimetres in one Litre, and we also know that there are 1,000,000 cubic centimetres in one cubic metre. Therefore 1 litre is the same as 1/1000th of a cubic metre i.e. 1 L = 0.001 m\(^3\) (i.e. there are 1000 litres in one cubic metre, not 10 as stated above). We are told that there are 65mg/Litre of Mercury, meaning that in every litre of water we will find 65 milligrams of mercury. Hence our measured mercury concentration becomes 65mg per thousandth of a cubic metre. So if we have exactly 1 cubic metre of water, we will have 65 x 1000 mg/m\(^3\) = 65,000 mg/m\(^3\) of mercury. Since there are 1000 milligrams per gram of substance, this quantity is the same as 65g/m\(^3\). But we will ultimately be wanting the answer in kilograms. There are 1000 grams per kilogram, so the above quantity becomes 0.065 kg/m\(^3\). Remember that this means that there will be 0.065 kg of mercury in every cubic metre of water. We are now ready to work out the total amount of mercury in the tank. To do so we need to calculate the volume of water in the tank. This is done by multiplying the width, height and depth of the tank. i.e. \[V= 90\times60\times9=48600\rm{m}^3\]Now from above we have calculated that there are 0.065 Kg in ever cubic metre of water, so we just multiply the concentration of mercury by the total volum of water to get the mass of mercury in the tank. i.e. \[0.065\rm{Kg/m}^3\times48600\rm{m}^3=3159\rm{kg}\] So there will be 3159 Kg of Mercury in the full tank of water. This is the long winded method to show you where the numbers come from, but you can do it quicker if you remember that there are 1,000,000 mg in 1 kilogram, and 1000 litres per metre cubed.