Identify all the elements involved in the reaction: potassium (K), chromium (Cr), oxygen (O), sodium (Na), sulfur (S), chlorine (Cl), and hydrogen (H).
Write down the unbalanced chemical equation: \(\mathrm{K_2CrO_4 + Na_2SO_3 + HCl \rightarrow KCl + Na_2SO_4 + CrCl_3 + H_2O}\).
Balance the chromium atoms first by ensuring the number of Cr atoms on both sides is equal. Since Cr appears in \(\mathrm{K_2CrO_4}\) and \(\mathrm{CrCl_3}\), adjust their coefficients accordingly.
Balance the potassium (K) and sodium (Na) atoms next by adjusting coefficients of \(\mathrm{K_2CrO_4}\), \(\mathrm{Na_2SO_3}\), \(\mathrm{KCl}\), and \(\mathrm{Na_2SO_4}\) to have equal numbers on both sides.
Balance the sulfur (S), chlorine (Cl), oxygen (O), and hydrogen (H) atoms last by adjusting the coefficients of \(\mathrm{Na_2SO_3}\), \(\mathrm{HCl}\), and \(\mathrm{H_2O}\), making sure the total number of each atom is the same on both sides of the equation.