(d) An aqueous solution of [tex]$2000 cm^3$[/tex] contains 53.0 g of sodium trioxocarbonate (IV). Calculate the concentration in
(i) [tex]$g / dm ^3$[/tex]
(ii) [tex]$mol / dm ^3$[/tex]
[ [tex]$Na =23, C =12, O =16$[/tex] ]
Answer (2)
The concentration of sodium trioxocarbonate (IV) in the solution is 26.5 g/dm³ and 0.25 mol/dm³.
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Convert the volume from c m 3 to d m 3 : 2000 c m 3 = 2 d m 3 .
Calculate the concentration in g / d m 3 : 2 d m 3 53.0 g = 26.5 g / d m 3 .
Calculate the molar mass of N a 2 C O 3 : 2 ( 23 ) + 12 + 3 ( 16 ) = 106 g / m o l .
Calculate the concentration in m o l / d m 3 : 2 d m 3 53.0 g /106 g / m o l = 0.25 m o l / d m 3 . The concentration is 26.5 d m 3 g and 0.25 d m 3 m o l .
Explanation
Problem Analysis We are given an aqueous solution of sodium trioxocarbonate (IV) ( N a 2 C O 3 ) with a volume of 2000 c m 3 and a mass of 53.0 g. We need to find the concentration in g / d m 3 and m o l / d m 3 . We are also given the molar masses of Na, C, and O.
Volume Conversion First, we need to convert the volume from c m 3 to d m 3 . Since 1 d m 3 = 1000 c m 3 , we have: V o l u m e = 2000 c m 3 = 1000 2000 d m 3 = 2 d m 3
Concentration in g/dm^3 (i) Now, we can calculate the concentration in g / d m 3 :
C o n ce n t r a t i o n ( g / d m 3 ) = V o l u m e ( d m 3 ) M a ss ( g ) = 2 d m 3 53.0 g = 26.5 g / d m 3
Molar Mass Calculation (ii) Next, we need to calculate the molar mass of N a 2 C O 3 :
M o l a r M a ss ( N a 2 C O 3 ) = 2 ∗ M ( N a ) + M ( C ) + 3 ∗ M ( O ) = 2 ∗ 23 + 12 + 3 ∗ 16 = 46 + 12 + 48 = 106 g / m o l
Moles Calculation Now, we can calculate the number of moles of N a 2 C O 3 :
M o l es ( N a 2 C O 3 ) = M o l a r M a ss ( g / m o l ) M a ss ( g ) = 106 g / m o l 53.0 g = 0.5 m o l
Concentration in mol/dm^3 Finally, we can calculate the concentration in m o l / d m 3 :
C o n ce n t r a t i o n ( m o l / d m 3 ) = V o l u m e ( d m 3 ) M o l es ( m o l ) = 2 d m 3 0.5 m o l = 0.25 m o l / d m 3
Final Answer Therefore, the concentration of the solution is 26.5 g / d m 3 and 0.25 m o l / d m 3 .
Examples
Understanding concentration is crucial in many real-life applications. For example, when preparing a cleaning solution, knowing the concentration ensures the solution is effective without being harmful. In cooking, the concentration of salt in a brine affects the flavor and preservation of food. In medicine, the concentration of a drug in the bloodstream determines its therapeutic effect. By calculating concentrations, we can accurately control the properties and effects of solutions in various practical scenarios.
