To determine which reaction shows a physical change, let's analyze each option.
A. [tex]\( \text{NaCl (s)} \rightarrow \text{NaCl (aq)} \)[/tex]
In this reaction, solid sodium chloride (NaCl) is dissolved in water to form an aqueous solution of NaCl. The dissolution process involves the separation of NaCl into its constituent ions, [tex]\( \text{Na}^+ \)[/tex] and [tex]\( \text{Cl}^- \)[/tex], in water. Importantly, there is no alteration of the chemical structure of NaCl; only its physical state changes from solid to aqueous. This represents a physical change.
B. [tex]\( 2 \text{CH}_3\text{OH} (\ell) + 3 \text{O}_2 (g) \rightarrow 2 \text{CO}_2 (g) + 4 \text{H}_2\text{O} (\Lambda) \)[/tex]
This equation describes the combustion of methanol ([tex]\( \text{CH}_3\text{OH} \)[/tex]) in the presence of oxygen ([tex]\( \text{O}_2 \)[/tex]), resulting in the formation of carbon dioxide ([tex]\( \text{CO}_2 \)[/tex]) and water ([tex]\( \text{H}_2\text{O} \)[/tex]). New products are formed as a result of this process, indicating a chemical change rather than a physical change.
C. [tex]\( 2 \text{AgNO}_3 (aq) + \text{CaBr}_2 (aq) \rightarrow 2 \text{AgBr} (s) + \text{Ca(NO}_3)_2 (aq) \)[/tex]
This reaction describes a precipitation reaction where aqueous solutions of silver nitrate ([tex]\( \text{AgNO}_3 \)[/tex]) and calcium bromide ([tex]\( \text{CaBr}_2 \)[/tex]) react to produce solid silver bromide ([tex]\( \text{AgBr} \)[/tex]) and aqueous calcium nitrate ([tex]\( \text{Ca}(\text{NO}_3)_2 \)[/tex]). The formation of new substances (silver bromide and calcium nitrate) indicates a chemical change.
D. [tex]\( \text{H}_2 (g) + \text{O}_2 (g) \rightarrow \text{H}_2\text{O} (M) \)[/tex]
This equation represents the reaction between hydrogen gas ([tex]\( \text{H}_2 \)[/tex]) and oxygen gas ([tex]\( \text{O}_2 \)[/tex]) to form water ([tex]\( \text{H}_2\text{O} \)[/tex]). The formation of water from hydrogen and oxygen gases is a chemical change.
Given this analysis, we can see that option A ([tex]\( \text{NaCl (s)} \rightarrow \text{NaCl (aq)} \)[/tex]) is the only reaction that represents a physical change since it involves a dissolution process without the formation of any new substances.
Thus, the correct answer is:
1.
