HS AP Chem question - mass % of each compound in a sample

[altay]

I am new to AP Chem and given a problem that I cannot begin to figure out how to compute. None of my calculations come up with the correct answer. How do I work through this?

PROBLEM: A sample containing NACl, SA2S04 and NAN03 (the number are sub), gives the following elemental analysis: NA: 32.08%; O: 36.01%; Cl: 19.51%. Calculate the mass percent of each compound in the sample?

How do I do this. My calculations are not coming out. Please help

 

[Gokul43201]

1. Unless you show us what effort you've made we can't help you. Please read the posting guidelines. We need to first see what thoughts or ideas you have.

2. What is "SA2SO4" (there's no such compound) ?

3. Henceforth, please post similar questions under the Homework & Coursework subforum.

 

[altay]

Challengenging

Sorry, not sure where to post everything. First time on site as user.

#2 should be NA2SO4

What I have done!

Cl: 12.42% 12.41/19.51 = 1.56 cl: 8.05 (8.051/8.02 = 1.00)
NACl - 58.14g
T=20.47%
A=32.14% NOTE This answer is supposed tobe32.17%

Na: 16.11% O=22.42 Na2SO4 = 142.05g
32.14+20.50=52.72 T=49.76%
A=20.58 45.69

0 .5.83 NaNO3 =.05 g
Na ? T 29.77%
A 15.45 27.39

Na 4/32.08% = 8.02%
O= 7/36.01% = 5.14%
Cl= 19.51%

S=x
N=y
TOTAL of S & N = 12.04

Total of all =100%
32.08
36.01
19.51
12.40

How do I figure out the mass percent of the sample?

Help: altay

 

[bomba923]

1) Welcome to PF

2) Generally, you would post such questions here. Also, you can sometimes ask PF moderators/admins to 'move' your thread to a more appropriate forum.

3) Your question can easily be solved via a system of linear equations, (although I'm not sure if that's what the AP Chemistry Exam prefers...). Letting m_X denote numerically the molar mass of the element 'X', the relative quantities of moles NaCl (x), Na₂SO₄ (y), NaNO₃ (z) can be calculated as the solution to

$$\begin{gathered} m_{{\text{Na}}} \left( {x + 2y + z} \right) = 32.08 \hfill \\ m_{\text{O}} \left( {4y + 3z} \right) = 36.01 \hfill \\ m_{{\text{Cl}}} x = 19.51 \hfill \\ \end{gathered}$$

Note that we can substitute x=19.51/m_Cl into the 2^nd and 3^rd equations,
and also (for convenience) rewrite them as:
$$\begin{gathered} 2y + z = 32.08m_{{\text{Na}}}^{ - 1} - 19.51m_{{\text{Cl}}}^{ - 1} \hfill \\ 4y + 3z = 36.01m_{{\text{O}}}^{ - 1} \hfill \\ \end{gathered}$$

Elimination (of these two equations) will allow us to immediately solve for both y and z, as
$$\begin{gathered} y = \frac{{3\left( {32.08m_{{\text{Na}}}^{ - 1} - 19.51m_{{\text{Cl}}}^{ - 1} } \right) - 36.01m_{\text{O}}^{ - 1} }} {{\text{2}}} \hfill \\ z = 36.01m_{\text{O}}^{ - 1} - 2\left( {32.08m_{{\text{Na}}}^{ - 1} - 19.51m_{{\text{Cl}}}^{ - 1} } \right) \hfill \\ \end{gathered}$$

"Plugging in" the molar masses values for Na, O, and Cl, we find that
x=0.5504
y=0.1414
z=0.5618

To find the mass percents of NaCl, Na₂SO₄, and NaNO₃, simply multiply the molar masses
of each compound by the relative molar quantities of each compound. Thus,

*Mass percent NaCl = 0.5504(58.44) = 32.17%
*Mass percent Na₂SO₄ = 0.1414(142.0) = 20.08%
*Mass percent NaNO₃ = 0.5618(84.99) = 47.75%
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Edit: You can check your answers for (x,y,z) on a graphing calculator via solving the
(augmented) matrix:
$$\left[ {\begin{array}{*{20}c} \hfill 1 & \hfill 2 & \hfill 1 & \hfill {\text{1.395}}} \\ \hfill 0 & \hfill 4 & \hfill 3 & \hfill {2.251} \\ \hfill 1 & \hfill 0 & \hfill 0 & \hfill {0.5504} \\ \end{array} } \right]$$

IIRC, the AP Chemistry Exam allows graphing calculators on the free response section, so you should have no trouble with these types of questions.

However, remember that graphing calculators do not usually consider significant figures when solving matrices.