To determine the correct chemical reaction for fluorine gas reacting with calcium metal at high temperatures to produce calcium fluoride powder, we need to examine the given options step-by-step:
1. [tex]$F_2(l) + Na(s) \longrightarrow NaF_2(s)$[/tex]
This reaction involves liquid fluorine ([tex]$F_2(l)$[/tex]) and sodium metal (Na). The product is sodium fluoride ([tex]$NaF_2$[/tex]) in solid form. Since the reactants are incorrect (lithium instead of gas and sodium instead of calcium), this equation cannot be correct.
2. [tex]$F_2(o) + Ca(c) \longrightarrow CaF_2(m)$[/tex]
This reaction is supposed to involve fluorine in an unknown state ('o') and solid calcium metal ('c'). The product is calcium fluoride ('m'). However, 'o' and 'm' are not standard states or forms in chemical notation, making this option incorrect.
3. [tex]$F_2(g) + Na(s) \xrightarrow{\Delta} NaF_2(l)$[/tex]
Here, fluorine gas ([tex]$F_2(g)$[/tex]) reacts with solid sodium metal (Na) at high temperatures (indicated by [tex]$\Delta$[/tex]), producing liquid sodium fluoride ([tex]$NaF_2(l)$[/tex]). Sodium is not the correct reactant, so this option is invalid for this reaction.
4. [tex]$F_2(g) + Ca(s) \xrightarrow{\Delta} CaF_2(s)$[/tex]
This reaction involves fluorine gas ([tex]$F_2(g)$[/tex]) and solid calcium metal (Ca) reacting at high temperatures (indicated by [tex]$\Delta$[/tex]) to produce solid calcium fluoride ([tex]$CaF_2$[/tex]). This matches precisely with the given problem statement, as it correctly identifies the reactants (fluorine gas and calcium metal) and the product (calcium fluoride powder).
Therefore, the correct formula equation for the reaction of fluorine gas with calcium metal to produce calcium fluoride is:
[tex]\[ \boxed{F_2(g) + Ca(s) \xrightarrow{\Delta} CaF_2(s)} \][/tex]
