Three solutions X,Y,Z of HCL are mixed to produce 100 ml of 0.1 M solution. The molarities of X, Y, Z are 0.07 M, 0.12 M and 0.15 M respectively. What respective volumes of X, Y and Z should be mixed?

Question

Arun · Answer

Dear student I am getting my answer as 55ml, 20 ml, 25 ml. Please let me know of this is correct then I will share my solution.

Khimraj · Answer

1. The amount of HCl in the resulting solution is the following: 𝑐𝑐(HCl) = 𝑛𝑛(HCl) 𝑉𝑉(solition) Consequently 𝑛𝑛(HCl) = 𝑐𝑐(HCl) · 𝑉𝑉(solition) = 100 𝑚𝑚𝑚𝑚 1000 · 0.1 𝑚𝑚𝑚𝑚𝑚𝑚 𝐿𝐿 = 0.01 𝑚𝑚𝑚𝑚𝑚𝑚 2. The volume of HCl in every solution is marked with x, y and z. We can write the equation: 𝑉𝑉Σ(HCl) = 𝑉𝑉𝑥𝑥(HCl) + 𝑉𝑉𝑦𝑦(HCl) + 𝑉𝑉𝑧𝑧(HCl) = 𝑥𝑥 + 𝑦𝑦 + 𝑧𝑧 = 0.1 𝐿𝐿 Or 𝑥𝑥 + 𝑦𝑦 + 𝑧𝑧 = 0.1 3. Then we write the formula for total amount of HCl: 𝑛𝑛Σ(HCl) = 𝑛𝑛𝑥𝑥(HCl) + 𝑉𝑉𝑦𝑦(HCl) + 𝑛𝑛𝑧𝑧(HCl) = 𝑐𝑐Σ(HCl) · 𝑛𝑛Σ(HCl) = 𝑐𝑐𝑥𝑥(HCl) · 𝑛𝑛𝑥𝑥(HCl) + 𝑐𝑐𝑦𝑦(HCl) · 𝑛𝑛𝑦𝑦(HCl) + 𝑐𝑐𝑧𝑧(HCl) · 𝑛𝑛𝑧𝑧(HCl) = 0.07𝑥𝑥 + 0.12𝑦𝑦 + 0.15𝑧𝑧 = 0.01 𝑚𝑚𝑚𝑚𝑚𝑚 Or 0.07𝑥𝑥 + 0.12𝑦𝑦 + 0.15𝑧𝑧 = 0.01 Or 7𝑥𝑥 + 12𝑦𝑦 + 15𝑧𝑧 = 1 4. The elimination of variable x it can be expressed by y, that is the solution Z is substituted by Y by way of coefficient expressed by ratio of respective molarities: 𝑐𝑐𝑧𝑧(HCl) 𝑐𝑐𝑦𝑦(HCl) = 1.25 Consequently, 𝑧𝑧 = 1.25𝑦𝑦 5. The set of equations can be composed: � 𝑥𝑥 + 𝑦𝑦 + 𝑧𝑧 = 0.1 7𝑥𝑥 + 12 + 15𝑧𝑧 = 1 If 𝑧𝑧 = 1.25𝑦𝑦, then � 𝑥𝑥 + 𝑦𝑦 + 1.25𝑦𝑦 = 0.1 7𝑥𝑥 + 12𝑦𝑦 + 18.75𝑦𝑦 = 1 Then � 𝑥𝑥 + 2.25𝑦𝑦 = 0.1 7𝑥𝑥 + 30.75𝑦𝑦 = 1 � 𝑥𝑥 = 0.1 − 2.25𝑦𝑦 7𝑥𝑥 + 30.75𝑦𝑦 = 1 Then 7 · (0.1 − 2.25𝑦𝑦) + 30.75𝑦𝑦 = 1 0.7 − 15.75𝑦𝑦 + 30.75𝑦𝑦 = 1 15𝑦𝑦 = 0.3 𝑦𝑦 = 0.02 𝑧𝑧 = 1.25𝑦𝑦 = 0.025 𝑥𝑥 = 0.1 − 𝑦𝑦 − 𝑧𝑧 = 0.1 − 0.02 − 0.025 = 0.055 6. The volumes of solutions X, Y, Z are: 𝑉𝑉𝑥𝑥(HCl) = 0.055 𝐿𝐿 = 55 𝑚𝑚𝑚𝑚 𝑉𝑉𝑦𝑦(HCl) = 0.025 𝐿𝐿 = 25 𝑚𝑚𝑚𝑚 𝑉𝑉𝑧𝑧(HCl) = 0.020 𝐿𝐿 = 20 𝑚𝑚𝑚𝑚 Answer: The volumes of X, Y, Z solutions are 0.055 L, 0.025 L and 0.020 L respectively.

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Three solutions X,Y,Z of HCL are mixed to produce 100 ml of 0.1 M solution. The molarities of X, Y, Z are 0.07 M, 0.12 M and 0.15 M respectively. What respective volumes of X, Y and Z should be mixed?

Three solutions X,Y,Z of HCL are mixed to produce 100 ml of 0.1 M solution. The molarities of X, Y, Z are 0.07 M, 0.12 M and 0.15 M respectively. What respective volumes of X, Y and Z should be mixed?

Three solutions X,Y,Z of HCL are mixed to produce 100 ml of 0.1 M solution. The molarities of X, Y, Z are 0.07 M, 0.12 M and 0.15 M respectively. What respective volumes of X, Y and Z should be mixed?

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Three solutions X,Y,Z of HCL are mixed to produce 100 ml of 0.1 M solution. The molarities of X, Y, Z are 0.07 M, 0.12 M and 0.15 M respectively. What respective volumes of X, Y and Z should be mixed?

Three solutions X,Y,Z of HCL are mixed to produce 100 ml of 0.1 M solution. The molarities of X, Y, Z are 0.07 M, 0.12 M and 0.15 M respectively. What respective volumes of X, Y and Z should be mixed?

Three solutions X,Y,Z of HCL are mixed to produce 100 ml of 0.1 M solution. The molarities of X, Y, Z are 0.07 M, 0.12 M and 0.15 M respectively. What respective volumes of X, Y and Z should be mixed?

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