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mathematics

Nitrate

Nitrate is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Nitrate rather than just read about it. In short: Nitrate is a polyatomic ion with the chemical formula NO3−. Salts containing this ion are called nitrates.

Nitrate — main illustration
Nitrate — illustration

Key takeaways

  • Nitrate belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Nitrate to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Nitrate from memory before moving on to harder problems.

Reference excerpt

Nitrate is a polyatomic ion with the chemical formula NO3−. Salts containing this ion are called nitrates. Nitrates are common components of fertilizers and explosives. Almost all inorganic nitrates are soluble in water. An example of an insoluble (inorganic) nitrate is bismuth oxynitrate. In nature, nitrates are produced by a number of species of nitrifying bacteria in the natural environment using ammonia or urea as a source of nitrogen and source of free energy. Nitrate compounds for gunpowder were historically produced, in the absence of mineral nitrate sources, by means of various fermentation processes using urine and dung. Modern nitrate production is mostly focused on creation for fertilizer and chemical manufacturing for various applications, such as medicine synthesis, ceramics and preservation of meat. Annually, about 195 million metric tons of synthetic nitrogen fertilizers are used worldwide, with nitrates constituting a significant portion of this amount. Because nitrates are soluble and easily can be swept away from the soil because of precipitation, excessive agricultural use has been associated with nutrient runoff, water pollution, and the proliferation of aquatic dead zones. Direct exposure of nitrates for humans can have direct health consequences: the excess consumption of nitrates in cured meats is associated with intestinal cancers.

Chemical structure

The nitrate anion is the conjugate base of nitric acid, consisting of one central nitrogen atom surrounded by three identically bonded oxygen atoms in a trigonal planar arrangement. The nitrate ion carries a formal charge of −1. This charge results from a combination formal charge in which each of the three oxygens carries a −2⁄3 charge, whereas the nitrogen carries a +1 charge, all these adding up to formal charge of the polyatomic nitrate ion. This arrangement is commonly used as an example of resonance. Like the isoelectronic carbonate ion, the nitrate ion can be represented by three resonance structures:

Chemical and biochemical properties In the NO3− anion, the oxidation state of the central nitrogen atom is V (+5). This corresponds to the highest possible oxidation number of nitrogen. Nitrate is a potentially powerful oxidizer as evidenced by its explosive behaviour at high temperature when it is detonated in ammonium nitrate (NH4NO3), or black powder, ignited by the shock wave of a primary explosive. In contrast to red fuming nitric acid (HNO3/N2O4), or concentrated nitric acid (HNO3), nitrate in aqueous solution at neutral or high pH is only a weak oxidizing agent in redox reactions in which the reductant does not produce hydrogen ions (such as mercury going to calomel). However, it is still a strong oxidizer when the reductant does produce hydrogen ions, such as in the oxidation of hydrogen itself. Nitrate is stable in the absence of microorganisms, or reductants such as organic matter. In fact, nitrogen gas is thermodynamically stable in the presence of 1 atm of oxygen only in very acidic conditions, and otherwise would combine with it to form nitrate. This is shown by subtracting the two oxidation reactions:

N2 + 6 H2O → 2 NO3− + 12 H+ + 10 e− E 0 = 1.246 − 0.0709 pH + 0.0591 10 log ⁡ ( N O 3 − ) 2 P N 2 {\displaystyle \qquad E_{0}=1.246-0.0709{\text{ pH }}+{\frac {0.0591}{10}}\log {\frac {(\mathrm {NO_{3}^{-}} )^{2}}{P_{\mathrm {N_{2}} }}}}

2 H2O → O2 + 4 H+ + 4 e− E 0 = 1.228 − 0.0591 pH + 0.0591 4 log ⁡ P O 2 {\displaystyle \qquad \qquad \qquad E_{0}=1.228-0.0591{\text{ pH }}+{\frac {0.0591}{4}}\log {P_{\mathrm {O_{2}} }}}

giving:

2 N2 + 5 O2 + 2 H2O → 4 NO3− + 4 H+ 0 = 0.018 − 0.0118 pH + 0.0591 10 log ⁡ ( N O 3 − ) 2 P N 2 − 0.0591 4 log ⁡ P O 2 {\displaystyle \qquad 0=0.018-0.0118{\text{ pH }}+{\frac {0.0591}{10}}\log {\frac {(\mathrm {NO_{3}^{-}} )^{2}}{P_{\mathrm {N_{2}} }}}-{\frac {0.0591}{4}}\log {P_{\mathrm {O_{2}} }}}

Dividing by 0.0118 and rearranging gives the equilibrium relation:

… excerpt ends here. Continue reading the full article.

Illustrations

Nitrate illustration
Nitrate: The nitrate ion with the partial charges shown
The nitrate ion with the partial charges shown
Nitrate illustration
Nitrate: Sea surface nitrate from the World Ocean Atlas
Sea surface nitrate from the World Ocean Atlas
Nitrate: Excessive nitrate and phosphate concentrations measured in the Pacific Ocean[39]
Excessive nitrate and phosphate concentrations measured in the Pacific Ocean[39]

Worked examples

Example 1 — a first encounter with Nitrate

Start with the simplest possible case. Write down what Nitrate claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Nitrate before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Nitrate ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Nitrate

In research
Nitrate appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Nitrate in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Nitrate is common in secondary-school and first-year university syllabi. It links to neighbouring topics Curing agents, Functional groups, Garde manger, so understanding it makes those chapters shorter.
In everyday life
Look for Nitrate outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Nitrate in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Nitrate means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Nitrate out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Nitrate in simple terms?

Nitrate is a polyatomic ion with the chemical formula NO3−. Salts containing this ion are called nitrates.

Why does Nitrate matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Nitrate?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Nitrate.

Tags

  • Curing agents
  • Functional groups
  • Garde manger
  • Nitrates
  • Nitrogen cycle
  • Nitrogen oxyanions
  • Non-coordinating anions
  • Water quality indicators

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