Let's work through the problem step by step.
- For the compound
PQ2, its molar mass is
MPQ2=MP+2MQ When 1 g of
PQ2 is dissolved in 51 g ( 0.051 kg ) of benzene, the molality is:
m1=‌The freezing point depression is given by:
∆Tf=Kf⋅m For benzene,
Kf=5.1K‌kg‌mol−1. Thus,
0.8=5.1×‌.Notice that:
‌=100 so the equation simplifies to:
‌=0.8Solving for
MP+2MQ :
MP+2MQ=‌=125 Again, 1 g of
PQ3 in 51 g benzene gives a molality:
m2=‌and the freezing point depression is:
0.625=5.1×‌ This simplifies similarly to:
‌=0.625.Thus,
MP+3MQ=‌=160 - Now, subtract equation (1) from equation (2):
(MP+3MQ)−(MP+2MQ)=160−125which gives:
MQ=35 - Substitute
MQ=35 back into equation (1):
MP+2(35)=125‌‌⇒‌‌MP+70=125so,
MP=125−70=55.Thus, the atomic masses are:
‌MP=55‌MQ=35Looking at the options provided, the correct answer is Option D: 55,35 .