consider the reaction N2O5 + h2o -> 2HNO3 how many moles of N2O5 must be dissolved into one more of H2O to obtain an aqueous solution of HNO3 in which the mole fraction of HNO3 is 0.5
N2O5 + H2O ==> 2HNO3
If you want XHNO3 = 0.5 and mols H2O to be 1.0, then mols HNO3 must be 1.0.
XHNO2 = 1.0 mol HNO3/2 mol total = 0.5
To obtain 1 mol HNO3 will require only 1/2 mol N2O5.
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To find the number of moles of N2O5 required to obtain an aqueous solution of HNO3 with a mole fraction of 0.5, we need to use the concept of mole fraction and stoichiometry.
1. Start by writing the balanced equation for the reaction:
N2O5 + H2O -> 2HNO3
2. The mole fraction of HNO3 (X_HNO3) is defined as the moles of HNO3 divided by the total moles of all species in the solution. In this case, we want X_HNO3 to be 0.5.
3. Let's assume we dissolve x moles of N2O5 in one mole of H2O. Since the stoichiometry ratio between N2O5 and HNO3 is 1:2, we will have 2x moles of HNO3 formed.
4. Now, we can set up the equation for mole fraction:
X_HNO3 = moles of HNO3 / (moles of N2O5 + moles of H2O)
5. Substituting the values, we have:
0.5 = 2x / (x + 1)
6. Multiply both sides of the equation by (x + 1):
0.5(x + 1) = 2x
7. Distribute and simplify:
0.5x + 0.5 = 2x
8. Subtract 0.5x from both sides:
0.5 = 1.5x
9. Divide both sides by 1.5:
0.5 / 1.5 = x
10. Solve for x:
x = 0.33
Therefore, approximately 0.33 moles of N2O5 must be dissolved into one mole of H2O to obtain an aqueous solution of HNO3 with a mole fraction of 0.5.