Upon decomposition, one sample of magnesium fluoride produced 1.64 kg of magnesium and 2.56 kg of fluorine. A second sample produced 1.29 kg of magnesium. How much fluorine (in grams) did the sample produce?

4.20 kg

You don't even need the for this one, all you need to use to solve this problem is the .

So, the first sample produced ##"1.64 kg"## of magnesium and ##"2.56 kg"## of fluorine. Since the combined mass of the products must equal the mass of the reactant, you'll have

##m_("magnesium fluoride") = 1.64 + 2.56 = "4.20 kg"##

Out of this,

##("1.64 kg")/("4.20 kg")*100% = 39%## by mass is magnesium, and

##("2.56 kg")/("4.20 kg")*100% = 61%## by mass is fluorine.

Since the same compound undergoes decomposition in the second reaction, the same proportions by mass will be true for both magnesium, and fluorine. So, the second sample produces ##"1.29 kg"## of magnesium, which means that

##"1.29 kg" * 100/39 = 3.31## ##"kg"## of magnesium fluoride is in the second sample, which means that

##"3.31 kg" * 61/100 = 2.02## ##"kg"## of fluorine will be produced this time.

Verify that the mass is conserved by

##"3.31 kg" = "1.29 kg" + "2.02 kg"##, which confirms the calculations for fluorine and for the magnesium fluoride.