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Some Basic Concepts of Chemistry question

2019 · 12 Apr · Shift 1 · Q5
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Some Basic Concepts of Chemistry question

2019 · 12 Apr · Shift 1 · Q5

JEE MainChemistrySome Basic Concepts of ChemistryMCQ+4 / −1
5 moles of AB2AB_2AB2​ weigh 125 × 10–3 kg and 10 moles of A2B2A_2B_2A2​B2​ weigh 300 × 10–3 kg. The molar mass of A (MA) and molar mass of B (MB) in kg mol are:
  1. A
    MA = 10 × 10–3 and MB = 5 × 10–3
  2. B
    MA = 25 × 10–3 and MB = 50 × 10–3
  3. C
    MA = 5 × 10–3 and MB = 10 × 10–3
  4. D
    MA = 50 × 10–3 and MB = 25 × 10–3
View written solutionFree

Correct answer: C

  1. Form equations from given molar masses

Let molar masses of AAA and BBB be MAM_AMA​ and MBM_BMB​ in kg mol−1\text{kg mol}^{-1}kg mol−1.

For AB2AB_2AB2​: M(AB2)=MA+2MBM(AB_2)=M_A+2M_BM(AB2​)=MA​+2MB​ Given 5 moles weigh 125×10−3125\times10^{-3}125×10−3 kg, so molar mass is M(AB2)=125×10−35=25×10−3 kg mol−1M(AB_2)=\frac{125\times10^{-3}}{5}=25\times10^{-3}\ \text{kg mol}^{-1}M(AB2​)=5125×10−3​=25×10−3 kg mol−1 Hence, MA+2MB=25×10−3...(1)M_A+2M_B=25\times10^{-3} \quad ...(1)MA​+2MB​=25×10−3...(1)

  1. Use the second compound

For A2B2A_2B_2A2​B2​: M(A2B2)=2MA+2MBM(A_2B_2)=2M_A+2M_BM(A2​B2​)=2MA​+2MB​ Given 10 moles weigh 300×10−3300\times10^{-3}300×10−3 kg, so molar mass is M(A2B2)=300×10−310=30×10−3 kg mol−1M(A_2B_2)=\frac{300\times10^{-3}}{10}=30\times10^{-3}\ \text{kg mol}^{-1}M(A2​B2​)=10300×10−3​=30×10−3 kg mol−1 Thus, 2MA+2MB=30×10−32M_A+2M_B=30\times10^{-3}2MA​+2MB​=30×10−3 Dividing by 2: MA+MB=15×10−3...(2)M_A+M_B=15\times10^{-3} \quad ...(2)MA​+MB​=15×10−3...(2)

  1. Solve the equations

Subtract (2) from (1): (MA+2MB)−(MA+MB)=25×10−3−15×10−3(M_A+2M_B)-(M_A+M_B)=25\times10^{-3}-15\times10^{-3}(MA​+2MB​)−(MA​+MB​)=25×10−3−15×10−3 MB=10×10−3 kg mol−1M_B=10\times10^{-3}\ \text{kg mol}^{-1}MB​=10×10−3 kg mol−1

Now from (2): MA+10×10−3=15×10−3M_A+10\times10^{-3}=15\times10^{-3}MA​+10×10−3=15×10−3 MA=5×10−3 kg mol−1M_A=5\times10^{-3}\ \text{kg mol}^{-1}MA​=5×10−3 kg mol−1

  1. Match with options

So, MA=5×10−3 kg mol−1,MB=10×10−3 kg mol−1M_A=5\times10^{-3}\ \text{kg mol}^{-1}, \qquad M_B=10\times10^{-3}\ \text{kg mol}^{-1}MA​=5×10−3 kg mol−1,MB​=10×10−3 kg mol−1 This matches Option C.

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