This question involves identifying which chemical reactions produce propane (C₃H₈) as a major product. Propane is an alkane, so we are looking for reactions that yield alkanes through processes like decarboxylation, reduction, or hydrolysis.

Step 1: Analyze Each Reaction

We need to evaluate each given reaction one by one to see if propane is formed.

Reaction 1: ${CH}_{3} CH 2 COONa + NaOH \overset{CaO, Δ}{\to} {CH}_{3} {CH}_{3} + {Na}_{2} {CO}_{3}$
This is the decarboxylation of sodium butanoate. The general reaction for decarboxylation of a sodium salt of a carboxylic acid is: $R - COONa + NaOH \overset{CaO, Δ}{\to} R - H + {Na}_{2} {CO}_{3}$ . Here, R is C₃H₇ (propyl group), so the alkane produced is propane (C₃H₈). This reaction produces propane.

Reaction 2: ${CH}_{3} {CH}_{2} {CH}_{2} Br + Na / dry ether \to {CH}_{3} {CH}_{2} {CH}_{2} {CH}_{2} {CH}_{2} {CH}_{3}$
This is the Wurtz reaction. Alkyl halides react with sodium in dry ether to form alkanes with twice the number of carbon atoms. Here, 1-bromopropane (C₃H₇Br) would yield hexane (C₆H₁₄), not propane.

Reaction 3: ${CH}_{3} C_{\equiv} C H + 2 H_{2} \overset{Ni}{\to} {CH}_{3} {CH}_{2} {CH}_{3}$
This is the catalytic hydrogenation of an alkyne. Propyne (CH₃C≡CH) on complete hydrogenation gives propane. This reaction produces propane.

Reaction 4: ${CH}_{3} {CH}_{2} MgBr + {CH}_{3} OH \to {CH}_{3} {CH}_{2} {CH}_{3} + Mg (O H) Br$
This is the reaction of a Grignard reagent with an alcohol. Grignard reagents (R-MgBr) react with alcohols (R'-OH) to give alkanes (R-H). Here, ethyl magnesium bromide (C₂H₅MgBr) reacts with methanol (CH₃OH) to give ethane (C₂H₆), not propane.

Step 2: Conclusion

Only Reaction 1 and Reaction 3 produce propane as the major product.

Related Topics and Formulae

Decarboxylation: $R - COONa + NaOH \overset{CaO, Δ}{\to} R - H + {Na}_{2} {CO}_{3}$
Applicable for sodium salts of carboxylic acids to yield alkanes with one less carbon.

Catalytic Hydrogenation of Alkynes: $R - C \equiv C - R' + 2 H_{2} \overset{Catalyst}{\to} R - {CH}_{2} - {CH}_{2} - R'$
Complete hydrogenation converts alkynes to alkanes.

Wurtz Reaction: $2 R - X + 2 Na \overset{dry ether}{\to} R - R + 2 NaX$
Produces symmetric alkanes with double the carbon chain length.

Grignard Reagent with Alcohol: $R - MgX + R' - OH \to R - H + R' - OMgX$
Produces alkane (R-H) from the Grignard reagent.