Question 9.13: Calculations Involving Solutions in Reactions How many milli......
Calculations Involving Solutions in Reactions
How many milliliters of a 0.250 M BaCl_2 solution are needed to react with 0.0325 L of a 0.160 M Na _2 SO _4 solution?
Na _2 SO _4(a q)+ BaCl _2(a q) \longrightarrow BaSO _4(s)+2 NaCl (a q)
STEP 1 State the given and needed quantities.
STEP 2 Write a plan to calculate the needed quantity.
liters of Na_2SO_4 solution \xrightarrow[]{\text{Molarity}} moles of Na _2 SO _4 \xrightarrow[]{\text{Mole–mole factor}} moles of BaCl_2
\xrightarrow[]{\text{Molarity}} liters of BaCl_2 solution \xrightarrow[]{\text{Metric factor}} milliliters of BaCl_2 solution
STEP 3 Write equalities and conversion factors including mole–mole and concentration factors.
\begin{aligned} & 1\ L \text { of solution }=0.160 \text { mole of } Na _2 SO _4 \\ & \frac{0.160\ mole\ Na _2 SO _4}{1\ L \text { solution }} \text { and } \frac{1\ L \text { solution }}{0.160 \text { mole } Na _2 SO _4} \end{aligned}
\begin{aligned}1 \text { mole of } Na _2 SO _4=1 \text { mole of } BaCl _2\\\frac{1\ mole\ Na_2SO_4}{1\ mole\ BaCl_2}\text{ and }\frac{1\ mole\ BaCl_2}{1\ mole\ Na_2SO_4}\end{aligned}
\begin{aligned} & 1\ L \text { of solution }=0.250\ mole \text { of } BaCl _2 \\ & \frac{0.250 \text { mole } BaCl _2}{1\ L \text { solution }} \text { and } \frac{1\ L \text { solution }}{0.250 \text { mole } BaCl _2} \\ & \end{aligned}
\begin{gathered} 1\ L =1000\ mL \\ \frac{1000\ mL }{1\ L } \text { and } \frac{1\ L }{1000\ mL } \end{gathered}
STEP 4 Set up the problem to calculate the needed quantity.
\begin{aligned} & 0.0325\ \cancel{L \text { solution }} \times \frac{0.160 \cancel{\text { mole } Na _2 SO _4}}{1\ \cancel{L \text { solution }}} \times \frac{1 \cancel{\text { mole } BaCl _2}}{1 \cancel{\text { mole } Na _2 SO _4}} \times \frac{1\ \cancel{L \text { selution }}}{0.250 \cancel{\text { mole } BaCl _2}} \times \frac{1000\ mL\ BaCl _2 \text { solution }}{1\ \cancel{L \text { solution }}} \\\\ & =20.8\ mL \text { of } BaCl _2 \text { solution } \end{aligned}
| ANALYZE THE
PROBLEM |
Given | Need | Connect |
| 0.0325 L of 0.160 M Na_2SO_4
solution, 0.250 M BaCl_2 solution |
milliliters of
BaCl_2 solution |
mole-mole
factor |
|
| Equation | |||
| Na _2 SO _4(a q)+ BaCl _2(a q) \longrightarrow BaSO _4( s )+2 NaCl (a q) | |||