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# Exercise 18 - Chapter 2

edited June 2018

Here is an exercise for people familiar with reaction equations: check that conditions (a), (b), (c), and (d) of Definition 2.2 hold.

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1.
edited April 2018

Let $$Mat$$ be the set of materials, $$\rightarrow$$ a reaction, and $$+$$ a mixture or combination of materials. Let $$0$$ signify nothing, e.g. no material. Then we have $$(Mat, \rightarrow, 0, +)$$ and

(a) $$2{H}{2}O \rightarrow 2{H}{2}O$$ and $$2Na \rightarrow 2Na$$, then $$2{H}{2}O + 2Na \rightarrow 2NaOH + {H}{2}$$

(b) $$0 + {H}{2}O = {H}{2}O + 0 = {H}_{2}O$$

(c) $$({H}{2}O + {H}{2}O) + 2Na = {H}{2}O + ({H}{2}O + 2Na)$$

(d) $$2{H}{2}O + 2Na = 2Na + 2{H}{2}O$$

But this doesn't express the "for all" quantification and I don't know how.

Comment Source:Let \$$Mat \$$ be the set of materials, \$$\rightarrow \$$ a reaction, and \$$+ \$$ a mixture or combination of materials. Let \$$0 \$$ signify nothing, e.g. no material. Then we have \$$(Mat, \rightarrow, 0, +) \$$ and (a) \$$2{H}_{2}O \rightarrow 2{H}_{2}O \$$ and \$$2Na \rightarrow 2Na \$$, then \$$2{H}_{2}O + 2Na \rightarrow 2NaOH + {H}_{2} \$$ (b) \$$0 + {H}_{2}O = {H}_{2}O + 0 = {H}_{2}O \$$ (c) \$$({H}_{2}O + {H}_{2}O) + 2Na = {H}_{2}O + ({H}_{2}O + 2Na) \$$ (d) \$$2{H}_{2}O + 2Na = 2Na + 2{H}_{2}O \$$ But this doesn't express the "for all" quantification and I don't know how.