User:IDave2/sandbox

Avogadro's Number = 6.022 × 10²³. ---

Each antacid tablet is mixed with 40 mL of 0.1 M HCl; this acidic solution is the same stuff that is in stomach acid and one antacid pill is nowhere near enough to neutralize all 40 mL of the acid.

${\begin{aligned}{\text{40 mL of 0.1 M HCl}}&={\text{40 mL solution}}\times {\frac {\text{0.1 mole of HCl}}{\text{1 L solution}}}\\&=40\ {\underline {\text{mL solution}}}\times {\frac {\text{0.1 mole of HCl}}{1000\ {\underline {\text{mL solution}}}}}\qquad {\text{(common units cancel)}}\\&={\frac {40}{1000}}\times {\text{0.1 mole of HCl}}\\&={\text{0.004 mole of HCl}}\\&=4\times 10^{-3}\ {\text{moles of HCl}}\end{aligned}}$

$n_{\mathbf {H} ^{+}}=n_{\mathbf {OH} ^{-}}$

or

$(M_{\mathbf {H} ^{+}})(V_{\mathbf {H} ^{+}})=(M_{\mathbf {OH} ^{-}})(V_{\mathbf {OH} ^{-}})$

${\begin{aligned}t'&=\gamma \ (t-vx/c^{2})\\x'&=\gamma \ (x-vt)\\y'&=y\\z'&=z,\end{aligned}}$

where

$\gamma ={\frac {1}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}$

${\frac {1}{2}}$