# 50 grams of acetic acid C2H4O2 are dissolved in 200 g of water. Calculate the weight % and mole fraction of the acetic acid in the solution

[latex]50g[/latex] [latex]of[/latex] [latex] C_2H_4O_2[/latex] [latex]in[/latex] [latex] 200g[/latex] [latex]H_2O[/latex] so: [latex] \frac{50}{200+50}+100\%= \frac{50*100}{250}\%=20\%[/latex] [latex]MW of acid = 2*C+4*H+2*O = 2*12+4*1+2*16=[/latex] [latex]=24+4+32=60g/mol[/latex] so: [latex]\frac{50g}{60g/mol}\approx0.83moles[/latex] it means that in [latex]50g[/latex] of acid there is [latex]\approx0.83[/latex]moles of acid [latex]MW of H_2O = 2*H+O=2*1+16=2+16=18g/mol[/latex] so: [latex]\frac{200g}{18g/mol}\approx11.11moles[/latex] it means that: in [latex]200g[/latex] of water there is [latex]\approx11.11[/latex]moles of water therefore: [latex] \frac{0.83mol}{11.11mol+0.83mol}= \frac{0.83mol}{11.94mol}=0.069[/latex] So your answers are: [latex]20\%[/latex] and the mole fraction is: [latex]0.069[/latex]