Someone help me with this please. Consider the chemical reaction aP4O10 + bCaF2

Question

Someone help me with this please.

Consider the chemical reaction aP4O10 + bCaF2 cPF5 + dCa3 (PO4)2, where a, b, c, and d are unknown positive integers. The reaction must be balanced; that is: the number of atoms of each element must be the same before and after the reaction. For example, because the number of oxygen atoms must remain the same. 10a = 8d. While there are many possible choices for a, b, c, and d that balance the reaction it is customary to use the smallest possible integers. Balance this reaction.

Explanation / Answer

Given aP4010 + bCaF2 -> cPF5 + dCa3(PO4)2

equate the calcium atoms we get

b= 3d

equate the flourine atoms we get

2b=5c

equate the oxygen atoms we get

10a=8d

5a=4d

equate the phosphorus atoms we get

4a=c + 2d

consider d=1

then b=3 ,c=6/5 ,a= 4/5

so when d=5 we get

b=15 ,c=6,a= 4

so the values are

a,b,c,d= 4,15,6,5

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