Final answer:
The balanced equation is 2 C2H2 (g) + 5 O2 (g) → 4 CO2 (g) + 2 H2O (g), with coefficients R=2, S=5, T=4, Y=2. This corresponds to Choice B.
Step-by-step explanation:
The question involves balancing the chemical equation C2H2 (g) + O2 (g) → CO2 (g) + H2O (g). To balance it, we need to ensure that there is an equal number of each type of atom on both sides of the equation.
Let's start with the carbons (C). Since we have 2 carbons in C2H2, we need 2 molecules of CO2 to balance it, which gives us T=2.
Next, we look at the hydrogens (H). There are 2 hydrogens in C2H2, which means we need 1 molecule of H2O to have 2 hydrogens, making Y=1.
Finally, for oxygen (O), we now have 2 (from CO2) + 1 (from H2O) = 3 oxygen atoms on the product side. Since each O2 molecule provides 2 oxygen atoms, we need 5/2 (¼) molecules of O2 to balance the oxygen atoms, which is not a whole number. To get whole numbers, we can double the coefficients of all substances, leading to 2 C2H2 + 5 O2 → 4 CO2 + 2 H2O. This means R=2, S=5, T=4, and Y=2.
The correct option is R=2, S=5, T=4, Y=2, which corresponds to Choice B in the given options.