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.

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## Comments

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TopNewestYou 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$H_2O=5+\frac{70x}{120+18x}$

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@Ishan Dasgupta Samarendra

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@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).

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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, $x_{sol}=\frac{m_{sa}}{m_t}$

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@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 $Y$?

Really sorry, I just checked and saw I had made a calculation error. Thanks so muchLog in to reply

$[Cr(H_2O)_4Cl_2]Cl$, in this case, the water molecule doesn't go into the solution.

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 exampleLog in to reply

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@Tanishq Varshney , @Raghav Vaidyanathan @Harshvardhan Mehta @Sandeep Bhardwaj Sir Please help me.

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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.

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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.

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We do not "un-notify" for deleted comments.

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A solution of FeCl3 is M/30 its molarity for Cl- ion will be

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M/10

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There cannot be a "number of moles" since a mole is a formula for calculating the atomic mass for CARBON13

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