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You have gone back in time and are working with Dalton on a table of relative masses. Following are his data:

0.602g gas A reacts with 0.295g gas B
0.172g gas B reacts with 0.401g gas C
0.320g gas A reacts with 0.374g gas C

a) Assuming simplest formulas (AB,BC,AC) construct a table of relative masses for Dalton.

b) Knowing some history of chemistry, you tell Dalton that if he determines the volumes of the gases reacted at constant temperature and pressure he need not assume simplest formulas. You collect the following data:

6 volumes gas A + 1 volume gas B -------> 4 volumes product
1 volume gas B + 4 volumes gas C --------> 4 volumes product
3 volumes gas A + 2 volumes gas C --------> 6 volumes product

Write the simplest balanced equations, and find the actual relative masses of the elements. Explain your reasoning.