%3Cp%3EEthane%20burns%20in%20oxygen%20to%20produce%20carbon%20dioxide%20and%20st

Question

%3Cp%3EEthane%20burns%20in%20oxygen%20to%20produce%20carbon%20dioxide%20and%20steam.%20The%0Achemical%20reaction%20is%20decribed%20using%20the%20notation%3C%2Fp%3E%0A%3Cp%3E%20%26nbsp%3B%20%3Cspan%20class%3D%22finalized_jax%22%3E%5C(x_%7B1%7DC_%7B2%7DH_%7B6%7D%20%2B%0Ax_%7B2%7DO_%7B2%7D%20-----%26gt%3B%20x_%7B3%7DCO_%7B2%7D%20%2B%20x_%7B4%7DH_%7B2%7DO%5C)%3C%2Fspan%3E%0A%26nbsp%3B%26nbsp%3B%3C%2Fp%3E%0A%3Cp%3EWhere%20the%20subscripts%20on%20the%20elements%20indicate%20the%20number%20of%0Aatoms%20in%20each%20molecule.%20Describe%20the%20subsspace%20of%20values%20that%20will%0Abalance%20the%20equation.%3C%2Fp%3E%0A%3Cp%3EHint%3A%20find%20the%20span%20of%20the%20chemical%20reaction%3C%2Fp%3E%0A%3Cp%3Eshow%20all%20your%20work.%3C%2Fp%3E%0A

Explanation / Answer

balancing number of C molecules:

2*x1=x3..(1)

balancing number of H molecules:

6*x1=2*x4...(2)

balancing number of O molecules:

2*x2=2*x3+x4..(3)

we have 3 equations and 4 unknowns.

let x1=k

x3=2*k

x4=3*k

x2=3.5*k

so solution set becomes:

k*(1,2,3,3.5)

or k1*(2,4,6,7)

where k1 is any integer(as we need x1,x2,x3, and x4 as integer)

so span is (2*k1,4*k1,6*k1,7*k1) where k1 is any integer

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