= Solution
\b[For complete neutralization, the required masses of anhydrous potassium carbonate, anhydrous sodium carbonate and magnesium oxide are in the ratio $138:106:40=69:53:20$.] Here “carbonate of potash” means <potassium carbonate>, “carbonate of soda” means <sodium carbonate>, and “caustic magnesia” means <magnesium oxide>, rather than <magnesium hydroxide> or a <magnesium carbonate> preparation. The <hydration state> of the <sodium carbonate> matters considerably.
Each <formula unit> of either <carbonate> consumes two <protons>; each <formula unit> of <magnesium oxide> also consumes two <protons>. Thus one <mole> of each <base> neutralizes one <mole> of <sulfuric acid> when the final <salts> are the normal <sulfates>:
$$
\begin{aligned}
\mathrm{K_2CO_3+H_2SO_4}&\longrightarrow\mathrm{K_2SO_4+CO_2+H_2O},\\
\mathrm{Na_2CO_3+H_2SO_4}&\longrightarrow\mathrm{Na_2SO_4+CO_2+H_2O},\\
\mathrm{MgO+H_2SO_4}&\longrightarrow\mathrm{MgSO_4+H_2O}.
\end{aligned}
$$
The <carbon dioxide> evolved in the first two <chemical reactions> escapes, whereas <magnesium oxide> produces no <gas>. The <stoichiometric coefficients>, rather than the visibly different behaviour of the <bases>, determine the required amounts.
Let $m$ be the <mass> of pure $\mathrm{H_2SO_4}$ in the given <chemical solution>. Using the rounded <relative atomic masses> $\mathrm{H}=1$, $\mathrm{C}=12$, $\mathrm{O}=16$, $\mathrm{Na}=23$, $\mathrm{Mg}=24$ and $\mathrm{K}=39$ gives
$$
\boxed{m_{\mathrm{K_2CO_3}}=\frac{138}{98}m,\qquad m_{\mathrm{Na_2CO_3}}=\frac{106}{98}m,\qquad m_{\mathrm{MgO}}=\frac{40}{98}m.}
$$
Thus 98 mass units of pure <sulfuric acid> require respectively 138, 106 and 40 mass units. Present <atomic weights> slightly change these rounded values, without changing the one-to-one <mole> ratios. If $m_s$ denotes the <mass> of the supplied <acid> and $w$ its <mass fraction> of $\mathrm{H_2SO_4}$, substitute $m=wm_s$. A <volume> alone is insufficient without its <concentration> or an equivalent <density> and composition.
If “carbonate of soda” is instead the crystalline decahydrate, <sodium carbonate decahydrate>, its rounded <molar mass> is $286\ \mathrm{g\,mol^{-1}}$, so the corresponding factor is $286/98$, rather than $106/98$. Likewise an impure <base> requires correction for its assayed content. The unspecified given quantity can therefore be handled exactly by proportional reasoning; no missing numerical measurement is needed.
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