Hello!
We have the following data:
m1 (solute mass) = 20 % m/m
M1 (Molar mass of solute) (NH4)2 SO4 = ?
m2 (mass of the solvent) = ? (in Kg)
First we find the solute mass (m1), knowing that:
20% m/m = 20g/100mL
20 ------ 100 mL (0,1 L)
y g --------------- 1 L
y = 20/0,1
y = 200 g -->
m1 = 200 g
Let's find Solute's Molar Mass, let's see:
M1 of (Nh4)2SO4
N = 2*14 = 28
H = (2*4)*1 = 8
S = 1*32 = 32
O = 4*16 = 64
----------------------
M1 of (Nh4)2SO4 = 28+8+32+64 =>
M1 = 132 g/molWe must find the volume of the solvent and therefore its mass (m2), let us see:
d = 1,117 g/mL
m = 200 g
v (volumen of solute) = ?
![d = \dfrac{m}{V} \to V = \dfrac{m}{d}](https://tex.z-dn.net/?f=d%20%3D%20%20%5Cdfrac%7Bm%7D%7BV%7D%20%5Cto%20V%20%3D%20%20%5Cdfrac%7Bm%7D%7Bd%7D%20)
![V = \dfrac{200\:\diagup\!\!\!\!g}{1,117\:\diagup\!\!\!\!g/mL} \to V = 179\:mL\:(volumen\:of\:solute)](https://tex.z-dn.net/?f=V%20%3D%20%20%5Cdfrac%7B200%5C%3A%5Cdiagup%5C%21%5C%21%5C%21%5C%21g%7D%7B1%2C117%5C%3A%5Cdiagup%5C%21%5C%21%5C%21%5C%21g%2FmL%7D%20%5Cto%20V%20%3D%20179%5C%3AmL%5C%3A%28volumen%5C%3Aof%5C%3Asolute%29)
<span>The solvent volume will be:
</span>
1000 -179 => V = 821 mL (volumen of disolvent)
If: 1 mL = 1g
<span>Then the mass of the solvent is:
</span>
m2 (mass of the solvent) = 821 g →
m2 (mass of the solvent) = 0,821 Kg
Now, we apply all the data found to the formula of Molality, let us see:
![\omega = \dfrac{m_1}{M_1*m_2}](https://tex.z-dn.net/?f=%5Comega%20%3D%20%20%5Cdfrac%7Bm_1%7D%7BM_1%2Am_2%7D%20)
![\omega = \dfrac{200}{132*0,821}](https://tex.z-dn.net/?f=%5Comega%20%3D%20%20%5Cdfrac%7B200%7D%7B132%2A0%2C821%7D%20)
![\omega = \dfrac{200}{108,372}](https://tex.z-dn.net/?f=%5Comega%20%3D%20%20%5Cdfrac%7B200%7D%7B108%2C372%7D%20)
![\boxed{\boxed{\omega \approx 1,8\:Molal}}\end{array}}\qquad\checkmark](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cboxed%7B%5Comega%20%5Capprox%201%2C8%5C%3AMolal%7D%7D%5Cend%7Barray%7D%7D%5Cqquad%5Ccheckmark)
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<span>Another way to find the answer:
</span>
We have the following data:
W (molality) = ? (in molal)
n (number of mols) = ?
m1 (solute mass) = 20 % m/m = 20g/100mL → (in g to 1L) = 200 g
m2 (disolvent mass) the remaining percentage, in the case: 80 % m/m = 800 g →
m2 (disolvent mass) = 0,8 Kg
M1 (Molar mass of solute) (NH4)2 SO4
N = 2*14 = 28
H = (2*4)*1 = 8
S = 1*32 = 32
O = 4*16 = 64
----------------------
M1 of (Nh4)2SO4 = 28+8+32+64 =>
M1 = 132 g/mol <span>Let's find the number of mols (n), let's see:
</span>
![n = \dfrac{m_1}{M_1}](https://tex.z-dn.net/?f=n%20%3D%20%20%5Cdfrac%7Bm_1%7D%7BM_1%7D%20%20)
![n = \dfrac{200}{132}](https://tex.z-dn.net/?f=n%20%3D%20%5Cdfrac%7B200%7D%7B132%7D)
![n \approx 1,5\:mol](https://tex.z-dn.net/?f=n%20%5Capprox%201%2C5%5C%3Amol)
Now, we apply all the data found to the formula of Molality, let us see:
![\omega = \dfrac{n}{m_2}](https://tex.z-dn.net/?f=%5Comega%20%3D%20%20%5Cdfrac%7Bn%7D%7Bm_2%7D%20)
![\omega = \dfrac{1,5}{0,8}](https://tex.z-dn.net/?f=%5Comega%20%3D%20%20%5Cdfrac%7B1%2C5%7D%7B0%2C8%7D%20)
I hope this helps. =)