Here's how to determine which compound has a larger percent by mass of sulfur:

1. Calculate the Molar Mass of Each Compound:

* H₂S₂O₃ (Thiosulfuric acid):

* 2(1.01 g/mol H) + 2(32.06 g/mol S) + 3(16.00 g/mol O) = 114.14 g/mol

* H₂S₂O₈ (Peroxydisulfuric acid):

* 2(1.01 g/mol H) + 2(32.06 g/mol S) + 8(16.00 g/mol O) = 194.14 g/mol

2. Calculate the Mass of Sulfur in Each Compound:

* H₂S₂O₃: 2(32.06 g/mol S) = 64.12 g/mol

* H₂S₂O₈: 2(32.06 g/mol S) = 64.12 g/mol

3. Calculate the Percent by Mass of Sulfur:

* H₂S₂O₃: (64.12 g/mol S / 114.14 g/mol compound) * 100% = 56.18%

* H₂S₂O₈: (64.12 g/mol S / 194.14 g/mol compound) * 100% = 33.03%

Conclusion:

H₂S₂O₃ (Thiosulfuric acid) has a larger percent by mass of sulfur (56.18%) compared to H₂S₂O₈ (Peroxydisulfuric acid) (33.03%).