Pregunta de Natural Sciences and their Technologies #019e354a
O soro caseiro serve para combater a desidratação por meio da reposição da água e sais minerais perdidos, por exemplo, por diarreia. Uma receita simples para a sua preparação consiste em utilizar duas colheres grandes (de sopa) de açúcar e duas colheres pequenas (de café) de sal de cozinha, dissolvidos em 2 L de água fervida, obtendo-se uma solução com concentração de íon sódio de 1,4 mg/mL.
Considere as massas molares: NaCl=58,5 g/mol; Na=23 g/mol.
Qual é o valor mais próximo da massa, em grama, de cloreto de sódio presente em uma única colher pequena?
0.7 g
1.8 g
2.8 g
3.6 g
7.0 g
Explicación Oficial / Explicaciones de la Comunidad
Analysis of the Composition of Homemade Serum
The correct answer is option A. D) 3.6 g.
1. Resolution Strategy
The problem gives us the final concentration of sodium ions (Na⁺) in the solution and asks for the mass of sodium chloride (NaCl) in a single spoonful. To solve this, we need to work backward:
- Calculate the total mass of sodium ions (Na⁺) present in the 2 L of the final solution. 2. Using the ratio of molar masses to find the total mass of sodium chloride (NaCl) which originated this quantity of sodium ions. 3. Divide the total mass of NaCl by 2, since the recipe uses... two spoons of salt.
2. Step 1: Calculation of the Total Mass of Sodium (Na⁺)
The statement indicates that the sodium ion concentration is 1.4 mg/mL and the total volume of the solution is 2 L.
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Convert the volume to mL: * Volume = 2 L = 2000 mL
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Calculate the total mass of Na⁺: * Mass = Concentration × Volume * Mass (Na⁺) = 1.4 mg/mL × 2000 mL = 2800 mg
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Convert the mass to grams (g): * Mass (Na⁺) = 2800 mg / 1000 = 2.8 g
Therefore, the 2 L solution contains a total of 2.8 g of sodium ions.
3. Step 2: Calculation of the Total Mass of Sodium Chloride (NaCl)
Now, we need to find out what mass of NaCl is needed to produce 2.8 g of Na⁺. We use the given molar masses:
- Molar mass of Na = 23 g/mol * Molar mass of NaCl = 58.5 g/mol
This means that in every 58.5 g of NaCl, we have 23 g of Na. We can set up a simple rule of three to find the mass of NaCl (X) corresponding to 2.8 g of Na:
| NaCl mass | Na mass | | :--- | :--- | | 58.5 g | 23 g | | X | 2.8 g |
Solving the proportion:
X * 23 = 58.5 * 2.8
X = (58.5 * 2.8) / 23
X = 163.8 / 23
X ≈ 7.12 g
Therefore, the total mass of NaCl dissolved in 2 L of water is approximately 7.12 g.
4. Step 3: Calculating the Mass of NaCl per Spoon
The recipe used two small spoons of salt to obtain this total mass of 7.12 g. To find the mass in a single spoonful, simply divide the total by 2:
- Mass per spoonful = Total mass of NaCl / 2 * Mass per spoonful = 7.12 g / 2 = 3.56 g
5. Conclusion
The calculated value for a single teaspoon of salt is 3.56 g. Comparing it to the alternatives, the closest value is 3.6 g.