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A compound with molecular mass 180 is acylated with CH$_3$COCl to yield a compound with molecular mass 390. How many amino ($-\text{NH}_2$) groups does the original compound contain?
Acylation: each $-\text{NH}_2$ reacts with CH$_3$COCl to introduce a $-\text{COCH}_3$ group ($M = 42$) and release HCl.
Net mass added per amino group $= 42 - 1 = 42$ (the $-H$ is replaced by $-\text{COCH}_3$)
Wait โ each NH$_2$ + CH$_3$COCl โ NH$\cdot$COCH$_3$ + HCl. Mass change per group $= 42 - 1 = +41$... more precisely: $-NH_2$ (16) becomes $-NHCOCH_3$ (58): increase = 42.
Increase in mass $= 390 - 180 = 210$
Number of amino groups $= \dfrac{210}{42} = \mathbf{5}$
Which of the following statements about marginal costing are correct?
- It assists in resource optimization when a limiting factor is present.
- It ensures decisions are based on the full absorption cost.
- It includes the apportionment of service department costs.
- It typically results in a lower inventory valuation compared to absorption costing.
Marginal costing focuses on variable costs (contribution), making it ideal for limiting factor analysis (1). Because it excludes fixed overheads from inventory, valuation is lower than absorption (4). Statements 2 and 3 refer to absorption costing.
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