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Chemistry doubt: help needed urgently

Please help me with this question. I have a test tomorrow and I cannot understand this concept

Problem: 70 grams of pure, hydrated \(MgSO_4\) is dissolved in 90 grams of \(H_2O\). If the mole fraction of the solute is 0.039, find the molecular formula of the solute.

My flawed attempt at a solution:

Let the solute be \(MgSO_4.xH_2O\)\[\] In 70 grams, the number of moles of the solute is \(\dfrac{70}{120+18x}\)\[\] In 90 grams, the number of moles of the solvent is \(\dfrac{90}{18}+\dfrac{70}{120+18x}\)\[\] Plugging these values into the formula for mole fraction and equating it to 0.039, I thought I would get the value of x as 7. Instead, I \(still\) seem to be getting approximately 12.\[\] Could somebody please help me solve this question? In general, when we have a hydrated solute in an aqueous solution, do we include the water of crystallisation in the total mass of available water while calculating the number of moles of water? Any help would be really, really appreciated.

Note by Ishan Dasgupta Samarendra
1 year, 8 months ago

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You have to take the water of crystallization as part of the solvent too. Once dissolved, the all the water of crystallization go into the solution, thus increasing the number of moles of water. Hence:

moles of\(H_2O=5+\frac{70x}{120+18x}\) Raghav Vaidyanathan · 1 year, 8 months ago

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@Raghav Vaidyanathan @Raghav Vaidyanathan Thanks a lot for your efforts! But I tried it that way and I'm still unable to get 7 (which was given as the correct answer). Ishan Dasgupta Samarendra · 1 year, 8 months ago

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@Ishan Dasgupta Samarendra Try again, I got the answer as \(7\). Here are some hints:

moles of salt\(m_{sa}=\frac{70}{120+18x}\)

moles of \(H_2O, m_{h}=5+\frac{70x}{120+18x}\)

Total number of moles, \(m_t=m_h+m_{sa}\)

Mole fraction of solute, \(x_{sol}=\frac{m_{sa}}{m_t}\) Raghav Vaidyanathan · 1 year, 8 months ago

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@Raghav Vaidyanathan Really sorry, I just checked and saw I had made a calculation error. Thanks so much @Raghav Vaidyanathan Truly grateful for your help! Just one last doubt please. Suppose \(X.Y\) was dissolved in solvent \(Y\). Then is it a rule that always \(.Y\) from \(X.Y\) will contribute to an increase in the number of moles of solvent \(Y\)? Ishan Dasgupta Samarendra · 1 year, 8 months ago

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@Ishan Dasgupta Samarendra In case of water of crystallization, yes this is true. I am not aware of other instances in which this might be true. Sometimes, water molecules can occur in a coordination sphere, for example \([Cr(H_2O)_4Cl_2]Cl\), in this case, the water molecule doesn't go into the solution. Raghav Vaidyanathan · 1 year, 8 months ago

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@Raghav Vaidyanathan Alright, thanks so much once again :D Ishan Dasgupta Samarendra · 1 year, 8 months ago

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A solution of FeCl3 is M/30 its molarity for Cl- ion will be Ashish Gaur · 1 year, 3 months ago

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Comment deleted May 22, 2015

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Comment deleted May 22, 2015

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@Ishan Dasgupta Samarendra On solving your equation, value of x comes out to be approx 12.5 (rounding off to 12). So, isn't the answer \(MgSO_4.12H_2O\) ? Sandeep Bhardwaj · 1 year, 8 months ago

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@Sandeep Bhardwaj No Sir, it unfortunately was answered as 7 (many people at my coaching center had got the answer as approx 12). Ishan Dasgupta Samarendra · 1 year, 8 months ago

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@Ishan Dasgupta Samarendra Okay, then may be the given answer is wrong. But I ain't pretty sure. Sandeep Bhardwaj · 1 year, 8 months ago

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@Ishan Dasgupta Samarendra Please reserve @ mentions for targeting of specific people when you know that they will be interested. For notes like this, just let it appear naturally in their feed, they will reply if they see it.
Avoid mass targeting of @ mentions to "random" people. If you really need to do so, then limit it to under 5 people.

Also, if you think that you can get around this decent behavior by "removing names" or "deleting comments", I would be forced to take more further action. Calvin Lin Staff · 1 year, 8 months ago

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@Calvin Lin Sir, I never meant to mass target people. At first, I @mentioned 4 people (if I am correct). However, then I thought it would be better to @mention a different set of people and thus deleted the previous comment. I had thought that if I had deleted the comment, then the people I had @mentioned would not get a notification. Ishan Dasgupta Samarendra · 1 year, 8 months ago

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@Ishan Dasgupta Samarendra np, thanks for explaining.

We do not "un-notify" for deleted comments. Calvin Lin Staff · 1 year, 8 months ago

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@Calvin Lin Alright Sir, thanks for telling me. Sorry for having inadvertently bothered you, Sir. Ishan Dasgupta Samarendra · 1 year, 8 months ago

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