Answer:
1) 0.009 61 g C; 2) 0.008 00 mol C
Step-by-step explanation:
You know that you will need a balanced equation with masses, moles, and molar masses, so gather all the information in one place.
M_r:     12.01               44.01
               C  + ½O₂ ⟶ CO₂
m/g:                            0.352
1) <em>Mass of C
</em>
Convert grams of CO₂ to grams of C
 44.01 g CO₂ = 12.01 g C
     Mass of C = 0.352 g CO₂ × 12.01 g C/44.01 g CO₂
     Mass of C = 0.009 61 g C
2) <em>Moles of C
</em>
Convert mass of C to moles of C.
      1 mol C = 12.01 g C
Moles of C = 0.00961 g C × (1 mol C/12.01 g C)
Moles of C = 0.008 00 mol C
All the carbon comes from Compound A, so there are 0.008 00 mol C in Compound A.