13) B

Mr of 2KHCO₃ = 2(39 + 1 + 12 + 48) = 200
moles of KHCO₃ = m/Mr = 50 ÷ 200 = 0.25

moles of K₂CO₃ = 0.25 ÷ 2 = 0.125
mass of K₂CO₃ = 0.125 x 138 = 34.5g

The loss in mass is calculated as the mass of the gases (H₂O and CO₂) produced.
Loss in mass = Mass of KHCO₃ – Mass of K₂CO₃ = 50-34.5 = 15.5g