Balance this equation. underline ( )CF_(4)+underline ( )Br_(2)-underline ( )CBr_(4)+underline ( )F_(2) 1,2,1,2 2,1,2,1 2,2,2,2 1,2,2,1

To balance the chemical equation, we need to ensure that the number of atoms of each element is the same on both sides of the equation. The equation given is:<br /><br />\[ \underline{\quad}CF_{4} + \underline{\quad}Br_{2} \rightarrow \underline{\quad}CBr_{4} + \underline{\quad}F_{2} \]<br /><br />Let's denote the coefficients (the numbers in front of the compounds) as \(a\), \(b\), \(c\), and \(d\) respectively. The equation becomes:<br /><br />\[ aCF_{4} + bBr_{2} \rightarrow cCBr_{4} + dF_{2} \]<br /><br />Now, we will balance the equation by adjusting these coefficients:<br /><br />1. Balance the carbon (C) atoms: Since there is one carbon atom on both sides, we can set \(a = c\).<br />2. Balance the bromine (Br) atoms: There are 2 bromine atoms in \(Br_{2}\) and 4 bromine atoms in \(CBr_{4}\). Therefore, we need 2 molecules of \(Br_{2}\) to balance the bromine atoms, so \(b = 2\).<br />3. Balance the fluorine (F) atoms: There are 4 fluorine atoms in \(CF_{4}\) and 2 fluorine atoms in \(F_{2}\). Therefore, we need 2 molecules of \(F_{2}\) to balance the fluorine atoms, so \(d = 2\).<br /><br />Now we have:<br /><br />\[ aCF_{4} + 2Br_{2} \rightarrow aCBr_{4} + 2F_{2} \]<br /><br />Since \(a = c\), we can choose \(a = 1\) to simplify the coefficients. Therefore, the balanced equation is:<br /><br />\[ 1CF_{4} + 2Br_{2} \rightarrow 1CBr_{4} + 2F_{2} \]