{"id":1140,"date":"2017-09-30T05:07:40","date_gmt":"2017-09-30T05:07:40","guid":{"rendered":"https:\/\/kellyfish.me\/?p=1140"},"modified":"2018-11-04T21:10:25","modified_gmt":"2018-11-04T21:10:25","slug":"chemical-reactions-in-numbers","status":"publish","type":"post","link":"https:\/\/kellyfish.me\/index.php\/2017\/09\/30\/chemical-reactions-in-numbers\/","title":{"rendered":"“Chemical Reactions” in Numbers"},"content":{"rendered":"

[latexpage]<\/span><\/p>\n

Fun Math for Girls
\n<\/span>By Kelly Tan<\/span><\/span><\/p>\n

\"\"<\/span><\/p>\n

If you think chemistry is fun, doing chemical experiments may help you learn both molecular formulas and mathematical concepts.<\/span><\/p>\n

It is easy to understand those formulas. Each molecule of sulfuric acid $H_2SO_4$, for example<\/span>\u00a0has two hydrogen (H)atoms, one sulfur (S) atom, and four oxygen (O) atoms.<\/span><\/span><\/p>\n

But did you know that in math, when you do prime factorization, you are also looking at the \u201cmolecular formula\u201d of a number? Prime factorization is a process that is similar to decomposing a molecule. The result of this decomposition is a formula that represents an integer in its prime factors, like $2^2$<\/span>\u00b73, which represents $2^2$\u00b73 = 12.<\/span><\/span><\/p>\n

So a prime number is equivalent to an atom in chemistry. A composite number is a number, like 12, that contains multiple prime factors. So composite numbers behave like a molecule in chemistry.<\/span><\/p>\n

When writing equations for chemical reactions, an extremely important task is to first balance the number of atoms in both sides of the equation. For example, we know a water molecule ($H_2O$<\/span>) is composed from hydrogen and oxygen. Does this equation looks right?<\/span><\/span><\/p>\n

$H_2$<\/span> + $O_2$<\/span> -> $H_2O$<\/span><\/span><\/p>\n

No, because the number of oxygen atoms are not balanced on both sides. The proper way to write would be:<\/span><\/p>\n

$H_2$<\/span> + $O$ -> $H_2O$<\/span><\/span><\/p>\n

or, since oxygen atoms always come in a pair, we have:<\/span><\/p>\n

2$H_2$<\/span> + $O_2$<\/span> -> 2$H_2O$<\/span><\/span><\/p>\n

When doing prime factorization, it is important to be balanced too. Consider this:<\/span><\/p>\n

$2^5$<\/span>\u00b7$3$\u00b7$3^6$<\/span> = $2^5$<\/span>\u00b7$3^7$<\/span><\/span><\/p>\n

There are five 2’s in both side of equation. So it is balanced. For 3’s, the left side has 1+6=7 many factors, so the right side must have seven 3’s also.<\/span><\/p>\n

This can be applied to variables too, like the following:<\/span><\/p>\n

$x^5$<\/span>\u00b7$x$\u00b7$y^6$<\/span> = $x^5$<\/span>\u00b7$y^7$<\/span><\/span><\/p>\n

The difference between chemical formulas and algebra is that you put the number of atoms in chemical formula as a subscript (the number below), while in algebra, you put the number of prime numbers as superscript (the number above). This number is called the exponent of the factor.<\/span><\/p>\n

Now try the following exercises:<\/span><\/p>\n

$x^3$ \u00b7 $y^2$ \u00b7 $y^4$ =<\/span><\/p>\n

$5^2$ \u00b7 $5$ \u00b7 $x^2$ =<\/span><\/p>\n

$x^3$ \u00b7 $3^2$ \u00b7 $y^2$ \u00b7 $x^3$ =<\/span><\/p>\n

$x^3$ \u00b7 $x^4$ =<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

[latexpage] Fun Math for Girls By Kelly Tan If you think chemistry is fun, doing chemical experiments may help you learn both molecular formulas and mathematical concepts. It is easy to understand those formulas. Each molecule of sulfuric acid $H_2SO_4$, for example\u00a0has two hydrogen (H)atoms, one sulfur (S) atom, and four oxygen (O) atoms. But […]<\/p>\n","protected":false},"author":1,"featured_media":1262,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[28],"tags":[],"class_list":["post-1140","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-articles"],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/kellyfish.me\/wp-content\/uploads\/2017\/09\/41khnhcGV9L.jpg?fit=500%2C284&ssl=1","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/posts\/1140","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/comments?post=1140"}],"version-history":[{"count":22,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/posts\/1140\/revisions"}],"predecessor-version":[{"id":1320,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/posts\/1140\/revisions\/1320"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/media\/1262"}],"wp:attachment":[{"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/media?parent=1140"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/categories?post=1140"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/tags?post=1140"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}