QuestionDecember 13, 2025

When the following equation is balanced, what is the sum of the coefficients? underline ( )C_(2)H_(4)+underline ( )O_(2)arrow underline ( )CO_(2)+underline ( )H_(2)O 11 7 6 8

When the following equation is balanced, what is the sum of the coefficients? underline ( )C_(2)H_(4)+underline ( )O_(2)arrow underline ( )CO_(2)+underline ( )H_(2)O 11 7 6 8
When the following equation is balanced, what is the sum of the coefficients?
underline ( )C_(2)H_(4)+underline ( )O_(2)arrow underline ( )CO_(2)+underline ( )H_(2)O
11
7
6
8

Solution
4.5(254 votes)

Answer

8 Explanation 1. Assign variables to coefficients Let aC_2H_4 + bO_2 \rightarrow cCO_2 + dH_2O. 2. Balance carbon atoms 2a = c \implies c = 2a 3. Balance hydrogen atoms 4a = 2d \implies d = 2a 4. Balance oxygen atoms 2b = 2c + d. Substitute c=2a, d=2a: 2b = 2(2a) + 2a = 4a + 2a = 6a \implies b = 3a 5. Choose smallest integer a Set a=1: b=3, c=2, d=2 6. Sum the coefficients 1+3+2+2=8

Explanation

1. Assign variables to coefficients<br /> Let $aC_2H_4 + bO_2 \rightarrow cCO_2 + dH_2O$.<br /><br />2. Balance carbon atoms<br /> $2a = c \implies c = 2a$<br /><br />3. Balance hydrogen atoms<br /> $4a = 2d \implies d = 2a$<br /><br />4. Balance oxygen atoms<br /> $2b = 2c + d$. Substitute $c=2a$, $d=2a$: $2b = 2(2a) + 2a = 4a + 2a = 6a \implies b = 3a$<br /><br />5. Choose smallest integer $a$<br /> Set $a=1$: $b=3$, $c=2$, $d=2$<br /><br />6. Sum the coefficients<br /> $1+3+2+2=8$
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