The following formulas are useful in many aspects of aquaria and aquaculture, they can be used to create solutions and calculate dilutions.  These formula use metric measures and try to keep it simple using common knowledge weights and measures.   Units      Unit Definitions Concentration Percent Concentration ( = parts per hundred) (W/W) (W/V) Percent Concentration ( = parts per hundred) V/V Concentration Parts per million (ppm) and Parts per billion (ppb) Dilutions Units As concentration represents a proportional relationship, you can select from a variety of units. For example, 1 milligram/millilitre is the same as 1 gram/litre, 1 microgram/microlitre, or 1 nanogram/nanolitre. It is also the same as 1000 milligrams/litre! Always try to select units that simplify your expressions. Unit Definitions milligram = mg = 1/1000 of a g or 10-3 g gram = g = 1000 mg kilogram = kg = 1000 g or 103 g millilitre = 1/1000 of a litre or 10-3l litre = l = 1000 ml ppt = parts per thousand = g/L (0.01ppt = 10 ppm) ppm = parts per million = mg/L (1ppm = 0.001ppt) ppb = parts per billion = ug/L (1 ppb = 0.001ppm) ppm = ppt * 1000 ppt = ppm/1000 w/v = weight (of solute) per final solution volume  v/v = volume (of reagent) per final solution volume mole = 6.023 x 1023 molecules molarity = moles per litre molar = M = term used to discuss the molarity of solutions (e.g., 2.5 M means 2.5 moles of solute dissolved in one litre) millimole = 1/1000 of a mole millimolar = mM = term used to discuss molarity in thousandths of a mole (e.g., a 20 mM solution contains 20/1000 = 0.02 moles per litre)   NOTE: It is critical that you report units for concentrations, amounts and volumes.  When you make calculations for dilutions you must not mix up the units. Eg: it doesn't work to write, V1 (160 millilitres) * C1(160 milligrams/litre = V2 (unknown) * C2(desired-3 grams/litre)   Concentration The concentration of any solution can be found by dividing the amount of solute by the amount of solvent.  The formula to calculate concentration is;     Amount of solute Concentration =     Amount of solvent Eg1: You have 10 grams of sucrose and dissolve this in 200 millilitres of water. What is the concentration of sucrose in the solution? Information given;  Amount of solvent  = 0.2litre, Amount of solute = 10g Information required; Concentration = ? Concentration=10 grams / 0.2 litre Concentration = 50 grams/litre   Percent Concentration ( = parts per hundred) (W/W) (W/V) Percent concentration always multiplies the ratio of solute to solvent by 100. Variations of percent concentrations depend on which unit is used to measure the amount of solute or solvent.  The formula used to calculate percent concentration is; Concentration   Amount of solute = 100   Amount of solvent If mass is used the concentration is called weight by weight or (W/W) If volume is used for the solvent then the ratio is weight by volume (W/V) A dry chemical is mixed as dry mass (g) per volume where #g/100 ml = percent concentration. A 10% sucrose (sugar) solution is equal to 10 g (sugar) dissolved in 100 ml of solvent (water).  The solid is measured based upon its weight (w) while the solvent is measured based upon its volume, the sugar solution discussed above should be labelled as 10% w/v sugar. Eg2:  To make a 3 % w/v NaCl solution 3.0 g NaCl are dissolved in 100 ml water (or the equivalent for whatever volume you needed).  If you want to make up less or more than 100 ml of solution, the proper amount of solute can be determined by multiplying the number of grams in a 1% w/v solution by the desired final volume divided by 100. Eg3: To make a 350 ml of 12% w/v NaCl in water, substitute values into the percentage concentration formula and use algebra to solve. Information given; Concentration = 12%, Amount of solvent  = 350ml Information required; Amount of solute 12/100=Amount of solute/350ml (12/100)*350= Amount of solute = 42 g So, dissolve 42 g of NaCl in 350ml water Eg4: Make up 15 ml of 0.05% w/v NaCl Information given; Concentration = .05%, Amount of solvent  =15ml Information required; Amount of solute (.05/100) =Amount of solute/15 (.05/100)*15 =Amount of solute = .0075g = 7.5mg So dissolve 0.0075 g NaCl in 15ml water Percent Concentration ( = parts per hundred) V/V When using liquid reagents the percent concentration is based upon volume per volume, i.e., # ml/100 ml.  The same formula is used for W/W W/V and V/V. Eg5: If you want to make 100ml of 70% v/v ethanol you would mix 70 ml of 100% ethanol with 30 ml water Making up volumes less than 100 ml is handled the same way as for solutions prepared from solids. Eg6: To make up 912 ml of 21.5% v/v AquaX, Information given; Concentration = 21.5%, Amount of solvent  =912ml Information required; Amount of solute (21.5 /100 ml) = Amount of solute/912 (21.5/100)*912=Amount of solute = 196.1ml The amount of solvent used is based upon the final volume, you must subtract the starting volume from the final to calculate it. 912 - 196.1 = 715.9ml So, mix 196.1 ml of AquaX with 715.9 ml of water and you'll have a 21.5% v/v solution Concentration Parts per million (ppm) and Parts per billion (ppb) The difference in calculations of parts per million or parts per billion is the factor used to multiply the ratio. The formulas for these are; Parts per million(ppm) Concentration   Amount of solute = 1,000,000   Amount of solvent Parts per billion(ppb) Concentration   Amount of solute = 1,000,000,000   Amount of solvent The ppm and ppb calculations are done exactly the same as the percent calculations above . Keep the following in mind when doing these calculations These calculations are usually weight by weight calculations and the units of mass must be the same for both solute and solvent. To help identify the solute from the solvent , remember the solvent is the substances doing the dissolving and in any solution is the larger portion. Eg7: Calculate the mass in grams of magnesium in a body (solute) if the body weights 50 Kg and the concentration is 4.0 ppm. Information given; Concentration = 4.0ppm, Amount of solvent  = 50kg = 50, 000g Information required; Amount of solute (mass of magnesium in grams) 4/1,000,000=Amount of Solute/50,000 (4/1,000,000)*50,000=Amount of Solute = 0.2 grams of magnesium   Dilutions When we concentrate or dilute a solution the amount of solute in the solution does not change (only the concentration changes). Eg8: A 1litre water solution containing 10g NaCl is diluted to a volume of 2 litres. How many grams of NaCl is in the new solution? As only water (the solvent) is added the same amount of NaCl is in the solution (10grams). We can say that; Amount of solute before dilution/concentration = Amount of solute after dilution/concentration We know that concentration is a ratio of amount of solute to amount of solvent; See Example 1.     Amount of solute Concentration =     Amount of solvent The concentration formula can be re-arranged to find amount of solute in solution; Amount of Solute = Concentration * Amount of solvent X = C1 * V1 Eg9:  A solution of sucrose (in water) with volume V1 of 200ml and concentration C1 of 50grams/litre. What is the total amount of sucrose in your solution? Information given; Concentration = 50 g/l, Amount of solvent  = .2litre = 200ml Information required; Amount of solute (mass of sucrose in grams) X = C1*V1 X = 50 grams/litre * 0.2 litre X = 10 grams sucrose.   We can then combine these formula to allow amount of solute, dilutions and concentrations to be found; Amount of Solute = Concentration (before)   * Volume (before)   = Concentration (after) * Volume (after)   X   C1 * V1 = C2 * V2 The form of the concentration does not matter since all concentrations are a ratio of amount of solute to solvent The units for volume must be the same however. Eg10:  A NaCl solution with a concentration of 50g/l and a volume of 200ml is diluted to a total volume of 2 litres.  What is the concentration of the new solution? Information given; Concentration before dilution(C1) = 50 g/l, Amount of solvent before dilution(V1)  = .2litre, Amount of solvent after dilution(V2) = 2litre Information required; Concentration after dilution (C2) C2*2 = 50*.2 C2 = (50*.2)/2 C2 = 5 grams per litre Eg11:  A NaCl solution with a concentration of 50g/l and a volume of 200ml is diluted to a total volume of 2 litres.  What is the concentration of the new solution? Information given; Concentration before dilution(C1) = 50 g/l, Amount of solvent before dilution(V1)  = .2litre, Amount of solvent after dilution(V2) = 2litre Information required; Concentration after dilution (C2) C2*2 = 50*.2 C2 = (50*.2)/2 C2 = 5 grams per litre Eg12:  You have a stock solution of known concentration(50g/l), you wish to know how much solvent and original solution are required to reach a predetermined concentration (30g/l) and volume (2ltr). Information given; Concentration before dilution(C1) = 50 g/l,  Amount of solvent after dilution(V2) = 2litre, Concentration after dilution (C2) = 30g/l Information required; Amount of solvent before dilution(V1)  = ?, Additional solvent required = (V2-V1)   50 grams/litre * V1 litre = 30grams/litre * 2 litre V1=(30*2)/50 V1= 1.2 litre, this is the amount of stock solution required V2-V1 = Additional solvent required 2 -1.2 = .8 litre, this is the amount of additional solvent required to reach given concentration.   Eg13:  Calculate the concentration in ppm of a solution of chlorine bleach created by diluting 500 ml of a 4.0 ppm solution with 300 ml of water? Information given; Concentration before dilution(C1) = 4ppm,  Amount of solvent after dilution(V2) = 800ml, Amount of solvent before dilution(V1)  = 500ml Information required; Concentration after dilution (C2) =? C1 = 4.0 ppm ; V1 = 500ml; C2 = ? ppm; V2 = 800ml; 4*500=C2*800 C2=(4*500)/800 = 2.5ppm