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Chapter 3: Problem 164

A sample containing \(\mathrm{NaCl}, \mathrm{Na}_{2} \mathrm{SO}_{4},\) and \(\mathrm{NaNO}_{3}\) gives the following elemental analysis: Na: 32.08 percent; O: 36.01 percent; Cl: 19.51 percent. Calculate the mass percent of each compound in the sample.

Short Answer

Expert verified
The mass percent of NaCl is around 58.44% and the mass percent of Na2SO4 is around 41.56% in the sample. This sample doesn't seem to contain NaNO3.

Step by step solution

01

Calculation of moles of sodium

Using the given mass percent, one can calculate the moles of each element by considering that percent mass is basically the grams of the element in 100 g of sample. So, the moles of sodium can be calculated by the formula:Moles of Na = Given mass percent / Atomic weight of NaHence, Moles of Na = 32.08 / 22.99 = 1.396 moles
02

Calculation of moles of other elements

Similarly, calculate the moles of other elements. Note that for sulfur and nitrogen, their presence indicates the presence of SO4 and NO3 groups respectively. Hence, while calculating moles for O, only the rest of the O will be considered. Here are the calculations:Moles of O = (36.01 - (4* mass percent of S + 3* mass percent of N)) / Atomic weight of O = (36.01 - (4*0 + 3*0)) / 16.00 = 2.25 molesMoles of Cl = Given mass percent / Atomic weight of Cl = 19.51 / 35.45 = 0.55 moles
03

Calculation of ratio of moles

The ratio of moles of Na, O and Cl gives information regarding their stoichiometry in the compounds. From above, the ratio of moles of Na:O:Cl becomes 1.39:2.25:0.55. But let's take the smallest value of moles among these, which is of Cl, and divide all values by it to get a simple whole number ratio.So, Na:O:Cl = 1.39/0.55 : 2.25/0.55 : 0.55/0.55 = 2.53 : 4.09 : 1.
04

Identify the compounds

The main assumption here is that all the Na is in the form of NaCl, Na2SO4 and NaNO3. The ratio tells us that the sample contains approximately Na2O4Cl, which seems to represent two Na ions in Na2SO4 and one Na ion in NaCl. Therefore, there doesn't seem to be any NaNO3 in the sample.
05

Calculation of mass percents of compounds

The mass percent of each compound can be calculated by determining the mass contribution in 100 g of sample and calculating its percentage:Mass percent of NaCl = (Moles of NaCl in 100g) x Molar mass of NaCl= 1 x (22.99 g/mol + 35.45 g/mol) = 58.44%Mass percent of Na2SO4 = (Moles of Na2SO4 in 100g) x Molar mass of Na2SO4= 1 x (2*22.99 g/mol + 32.06 g/mol + 4*16.00 g/mol) = 41.56%

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Most popular questions from this chapter

Without doing any detailed calculations, arrange the following substances in the increasing order of number of moles: \(20.0 \mathrm{~g} \mathrm{Cl}, 35.0 \mathrm{~g} \mathrm{Br},\) and\(94.0 \mathrm{~g} \mathrm{I}\)

Ammonia is a principal nitrogen fertilizer. It is prepared by the reaction between hydrogen and nitrogen.$$3 \mathrm{H}_{2}(g)+\mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)$$In a particular reaction, 6.0 moles of \(\mathrm{NH}_{3}\) were produced. How many moles of \(\mathrm{H}_{2}\) and how many moles of \(\mathrm{N}_{2}\) were reacted to produce this amount of \(\mathrm{NH}_{3} ?\)

Ammonia and sulfuric acid react to form ammonium sulfate. (a) Write an equation for the reaction. (b) Determine the starting mass (in grams) of each reactant if \(20.3 \mathrm{~g}\) of ammonium sulfate is produced and \(5.89 \mathrm{~g}\) of sulfuric acid remains unreacted.

The natural abundances of the two stable isotopes of hydrogen (hydrogen and deuterium) are \({ }_{1}^{1} \mathrm{H}\) : 99.985 percent and \({ }_{1}^{2} \mathrm{H}: 0.015\) percent. Assume that water exists as either \(\mathrm{H}_{2} \mathrm{O}\) or \(\mathrm{D}_{2} \mathrm{O} .\) Calculate the number of \(\mathrm{D}_{2} \mathrm{O}\) molecules in exactly \(400 \mathrm{~mL}\) of water. (Density \(=1.00 \mathrm{~g} / \mathrm{mL} .)\)

Calculate the percent composition by mass of all the elements in calcium phosphate \(\left[\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\right],\) a major component of bone.
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