Final answer:
The balanced chemical equation using the partial balancing method is K₂Cr₂O₇ + 14HBr = 2KBr + CrBr₃ + 7H₂O + 3Br₂, which corresponds to option c).
Step-by-step explanation:
To balance the chemical equation using the partial balancing method, we should first balance atoms of elements other than hydrogen and oxygen, then proceed with balancing these two. The original equation is K₂Cr₂O₇ + HBr = KBr + CrBr₃ + H₂O + Br₂. Firstly, we note that there are two potassium (K) atoms on the left, so we should have two K atoms on the right side, hence the coefficient of 2 in front of KBr. For chromium (Cr), we have two Cr atoms on both sides. Next, for oxygen (O), we have seven oxygen atoms on the left, so we'll need seven water (H₂O) molecules on the right to balance the oxygen. Now, we should balance the hydrogen (H); since we have 14 hydrogen atoms from the seven water molecules, we'll need 14 H+ from the 14 HBr molecules. Lastly, we need to balance bromine (Br). We have 14 bromine atoms from 14HBr on the left and 2 on the right from 2CrBr₃, we further have 2 bromine atoms in each Br₂ molecule and must adjust to accommodate the 14 atoms already present. This requires 3 Br₂ molecules as 2(2) + 3(2) = 14.
Combining all these balances, our balanced chemical equation is (K₂Cr₂O₇ + 14HBr = 2KBr + CrBr₃ + 7H₂O + 3Br₂), matching option c).