Exercise 1
Two jars on the same windowsill
Anush keeps two jars side by side. The first is filled straight from the tap in Avan. The second has had a bag of peat sitting in it for a month, which has stained the water the color of weak tea and pushed the pH down. She measures both with the same pen.
Given
- Jar one pH 7.2
- Jar two pH 5.2
- Both jars, same temperature, same day, same meter
Task. How many times more hydrogen ions does jar two hold than jar one? Answer with a number, not with the word "more".
The property of pH that makes this a one line answer is stated on materials and water.
Exercise 2
A laboratory report in the wrong unit
A school in Avan asks the city water laboratory for an analysis of its tap. The report comes back in the unit Armenian and Russian laboratories have always used, and the German degrees the school's test kit prints are nowhere on the page. The biology teacher wants to put a piece of limestone in the class tank and needs to know whether it will do anything at all.
Given
- Total hardness 1.25 mg-eq/L, Avan district tap water1
- The class tank has no carbon dioxide injection
Task. Convert the hardness to German degrees. Then say whether that water is above or below the general hardness a limestone rock can reach in a tank with no injection, and what that means for the teacher's rock.
The conversion factor and the uninjected ceiling are both on chemistry. The ceiling is stated a second way on what nobody tells you about water.
Exercise 3
The label on a bottle of spring water
Davit wants to know whether a bottled Armenian spring water would suit his shrimp better than the tap. The label prints the minerals in milligrams per liter, the way a food label does, and says nothing at all about hardness.
Given
- Calcium 31.0 mg/L
- Magnesium 9.5 mg/L
- For comparison Davtashen tap water, about 7.7 dGH1
Task. Work out the general hardness of the bottled water in German degrees. Is it harder or softer than the Davtashen tap?
Both divisors, one for calcium and one for magnesium, are printed in the units part of chemistry.
Exercise 4
Nine looks worse than it is, or better
Mariam reads a paper that recommends a limit for nitrate in fresh water, and it gives the limit in a unit her test kit does not use. Her kit, like almost every hobby kit sold, reports the nitrate ion. The paper, like almost every toxicology paper, reports nitrate nitrogen.
Given
- Kit reading 35 mg/L of nitrate ion
Task. Convert the reading to nitrate nitrogen. Then find the figure recommended for freshwater animals, and say how many times over it her tank is.
The conversion factor, where it comes from, and the recommended figure are all in the units part of chemistry.
Exercise 5
The cycle eats something nobody watches
Tigran is cycling a new tank without fish. He adds ammonia by hand and waits for the bacteria to arrive, and over the whole cycle the tank processes a total of 3.0 milligrams of ammonia nitrogen per liter. He tests ammonia and nitrite every day because that is what the forums told him to do. He never tests carbonate hardness, and one morning the pH has fallen off a cliff.
Given
- Tank volume 54 L
- Carbonate hardness at the start 4.0 dKH, measured with a drop kit
- Total ammonia nitrogen oxidised over the cycle 3.0 mg/L
- No water changes during the cycle
Task. How much carbonate hardness does the cycle destroy, in German degrees, and what is left at the end? Note that not every number above is needed.
Nitrification takes protons out of the carbonate, and the amount per milligram of nitrogen is given on chemistry. You will need one hardness conversion from the same page.
Exercise 6
A reading of 1.2, and a decision to make
The filter in a family tank in Arabkir was cleaned under a hot tap, which killed most of what was living in it. Four days later the ammonia test is clearly not zero. It is August, the flat is warm, and the family wants to know whether the fish are in danger tonight or merely uncomfortable.
Given
- Total ammonia nitrogen 1.2 mg/L
- Temperature 26 C
- pH 7.6
Task. Find the acid dissociation constant at this temperature, then the fraction of the total that is free ammonia, then the free ammonia concentration in milligrams per liter. Compare it with the figure at which free ammonia is generally said to begin damaging gill tissue, and give a verdict.
Two equations, one for the constant and one for the fraction, sit together in the ammonia part of chemistry, along with the damage figure. Watch the temperature unit the equation expects.
Exercise 7
The same tank, and a bottle of buffer
A neighbor tells the family that the fix for a sick tank is to raise the pH, and hands them a bottle of buffer. They add it. Nothing else changes: no water is taken out, nothing is added to the ammonia already in there, the heater stays where it was. By the evening the pH pen reads 8.4.
Given
- Total ammonia nitrogen 1.2 mg/L, unchanged
- Temperature 26 C, unchanged
- pH 8.4, after the buffer
Task. Recompute the free ammonia. By what factor has it risen compared with the answer to the previous exercise, and is the tank now above the damage figure? Say in one sentence why the neighbor's advice is dangerous.
Same two equations, same page: the ammonia part of chemistry. Nothing new is needed.
Exercise 8
The same jar, two cities
Two cousins set up identical jars of water on the same day, one in Yerevan and one in Batumi at the coast. Both are open to the room, both sit at the same temperature, and both are left long enough for the water to come into balance with the air above it. Neither has a plant in it, so nothing is using the carbon dioxide up.
Given
- Yerevan station pressure 887 hPa3
- Batumi sea level, 1013 hPa
- Temperature 22 C, both jars
- Carbon dioxide in the air 420 ppm4
Task. Work out the dissolved carbon dioxide in each jar, in milligrams per liter. Then say by what percentage the Yerevan jar is short of the coastal one, and why that percentage does not depend on the temperature.
Henry's law, its temperature correction, the constant it uses and the way a mixing ratio in parts per million becomes a partial pressure are all in the carbon dioxide part of chemistry. The molar mass of carbon dioxide is printed on the same page.
Exercise 9
Five percent more iron
A planted tank has pale new leaves with dark veins, which is what a plant short of iron looks like. The keeper does not want to double the iron and cause an algae bloom. She wants a small, deliberate increase, and she wants to know the dose before she pours anything. There are two bottles on the shelf: one is a chelated iron fertiliser, the other is plain iron sulfate sold for garden soil.
Given
- Tank volume 160 L
- Iron in the water now 0.12 mg/L
- Target 5 percent higher than that
- Chelated bottle 0.60 mg of iron per millilitre
- Tank pH 8.1, well aerated, filter running
Task. How many millilitres of the chelated fertiliser raise the iron by 5 percent? Then answer the second half: if she used the iron sulfate instead, what would happen to almost all of it at pH 8.1? Name the two reactions in order.
What iron does in oxygenated water above about pH 5, the two reactions, and which chelate is still working at this pH are on phosphate, iron, copper.
Exercise 10
A tank that is only ever topped up
A tank in Davtashen is filled from the tap and then never water changed. The owner is careful about topping up, and every week he pours in enough tap water to replace what evaporated. He is proud of how stable it looks. Nothing is leaving the tank except pure water vapour, and everything dissolved in what he adds stays behind.
Given
- Davtashen tap water 305 mg/L of dissolved solids1
- Evaporation 6 percent of the tank volume per week
- Topped up weekly with tap water, no water changes
- Armenian drinking water limit 1,000 mg/L total mineralisation2
Task. After how many weeks does the water in that tank pass the drinking water limit? Give the answer in weeks and then in months.
The relation between weeks, evaporation rate and concentration is derived on the water change arithmetic and restated on phosphate, iron, copper.
Exercise 11
How many Saturdays
Nitrate has crept up in a tank that gets fed generously. The keeper wants it under 20 on his kit and he changes water on Saturdays. His tap water is not nitrate free either, which is the part people forget, so every change brings a little back in.
Given
- Tank now 40 mg/L of nitrate ion
- Tap water 3 mg/L of nitrate ion, same kit
- Each change 30 percent of the volume
- Target below 20 mg/L
- Assume nothing is added or removed between changes
Task. What does the kit read after the first change? How many Saturdays does he need before the tank is under his target?
The idea that a change leaves most of the old water in place, and what that does to a concentration, is on water changes.
Exercise 12
The nitrogen the conditioner leaves behind
A city switches from chlorine to chloramine for the summer. A keeper does a large water change on a tank whose ammonia has read zero for months, treats the new water with a conditioner that reduces the chlorine, and is surprised to see a faint color on the ammonia test an hour later. Nothing died. He wants to know whether it should have.
Given
- Tank volume 60 L
- Water change 50 percent, tank ammonia zero beforehand
- Monochloramine in the tap water 1.2 mg/L
- Molar mass of monochloramine 51.5 g/mol
- Molar mass of nitrogen 14.0 g/mol
- Tank pH 7.9, temperature 25 C
Task. Work out the total ammonia nitrogen the change puts into the tank, in milligrams per liter. Then find what fraction of it is free ammonia at this pH and temperature, and decide whether the keeper was ever close to trouble. Say in one sentence what a conditioner does to the chlorine and what it does not do to the nitrogen.
What a reducing conditioner leaves behind is in the dechlorination part of chemistry, the ammonia equations are further up the same page, and why chloramine is used at all is on planning a tank.
Exercise 13
What one filling is worth to the filter
A bedroom tank cannot have an air pump in it, so the keeper stands an oxidator in the corner instead. It is a sealed flask of hydrogen peroxide with a ceramic tablet in the bottom, it makes no sound at all, and it releases oxygen slowly for weeks. He wants to know whether it is actually carrying the tank or whether it is decoration, and the first bill to check is the filter's, because nitrifying bacteria buy their oxygen before any fish does.
Given
- Tank volume 90 L
- Ammonia nitrogen the filter processes 65 mg per day
- One filling 200 g of a 12 percent hydrogen peroxide solution, by mass
- Refill interval 5 weeks
- Molar mass of hydrogen peroxide 34.015 g/mol
- Molar mass of oxygen gas 31.999 g/mol
Task. Four parts. How many grams of oxygen does nitrification consume per day? How many grams of oxygen does one filling release? What is the average delivery in grams per day, and what share of it does the filter alone take? Finally, express that delivery as milligrams per liter per day and compare it with the dissolved oxygen a saturated tank in Yerevan holds at 25 C.
The reaction inside the flask, the oxygen cost of nitrification per gram of nitrogen, and the Yerevan saturation figure are all on oxygen. Note that the catalyst tablet is not consumed, so it does not enter the arithmetic anywhere.
Exercise 14
The same keeper, and the bill for her oxygen
The keeper from the iron exercise works out that her chelated dose is gone within a day, and reads that the answer is to run carbon dioxide and let the pH sit lower. She does both at once, because she also wanted more oxygen for the fish: the injection settles the tank at a new pH, and an oxidator lifts the dissolved oxygen at the same time. Two changes, pulling in opposite directions on the same reaction.
Given
- pH before 8.1, after 6.7
- Dissolved oxygen before 5.0 mg/L, after 7.2 mg/L
- Temperature, iron concentration and everything else unchanged
Task. Using the rate law for the oxygenation of ferrous iron, work out the factor the pH change contributes and the factor the oxygen change contributes, then the net factor by which the loss of iron speeds up or slows down. Then answer two more: at the original oxygen level, what pH would have slowed the loss by exactly a hundred times? And in one sentence, using both terms of that rate law, say why a keeper who fixes a low oxygen reading with a spray bar aimed at the surface may find her plants go pale.
The rate law is printed on oxygen. Read the exponents carefully: one term is squared and one is not, and that asymmetry is the whole exercise. The same page explains what surface movement does to dissolved carbon dioxide.
