Chemistry Labs

Problem 4

An alloy consists of rubidium and one of the other alkali metals. A sample of 4.6 g of the alloy, when allowed to react with water, liberates 2.241 dm3^3 of hydrogen at STP. (a) Which alkali metal is the component of the alloy? (b) What is the composition of the alloy in % by mass? Relative atomic masses: Ar(Li)=7A_r(\text{Li}) = 7; Ar(Na)=23A_r(\text{Na}) = 23; Ar(K)=39A_r(\text{K}) = 39; Ar(Rb)=85.5A_r(\text{Rb}) = 85.5; Ar(Cs)=133A_r(\text{Cs}) = 133.
Step 3 of 4: Solve the two balances
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n(Rb)+n(Li)=0.2;85.5 n(Rb)+7 n(Li)=4.6⇒n(Rb)=0.0408,  n(Li)=0.1592 moln(\text{Rb}) + n(\text{Li}) = 0.2; \quad 85.5\,n(\text{Rb}) + 7\,n(\text{Li}) = 4.6 \Rightarrow n(\text{Rb}) = 0.0408,\; n(\text{Li}) = 0.1592\ \text{mol}
Analysis

Substituting n(Li)=0.2−n(Rb)n(\text{Li}) = 0.2 - n(\text{Rb}) into the mass balance: 85.5 n(Rb)+7(0.2−n(Rb))=4.685.5\,n(\text{Rb}) + 7(0.2 - n(\text{Rb})) = 4.6, giving n(Rb)=0.0408n(\text{Rb}) = 0.0408 mol and n(Li)=0.1592n(\text{Li}) = 0.1592 mol.