1. Write the reaction relation

3-Hydroxy propanal undergoes dehydration to form acrolein:

$\text{3-Hydroxy propanal} \rightarrow \text{Acrolein} + H_2O$

So, the mole ratio is:

$1 : 1$

That means 1 mole of 3-hydroxy propanal gives 1 mole of acrolein.

2. Use percentage yield

Given actual mass of acrolein obtained = $7.8\,\text{g}$

Percentage yield = $64\%$

So,

$\text{Actual yield} = \frac{64}{100} \times \text{Theoretical yield}$

Hence theoretical yield of acrolein is:

$\text{Theoretical yield} = \frac{7.8 \times 100}{64} = 12.1875\,\text{g}$

3. Convert theoretical acrolein mass to moles

Molar mass of acrolein = $56$

$n(\text{acrolein}) = \frac{12.1875}{56} = 0.21763\,\text{mol}$

Because of $1:1$ mole ratio,

$n(\text{3-hydroxy propanal}) = 0.21763\,\text{mol}$

4. Find required mass of 3-hydroxy propanal

Molar mass of 3-hydroxy propanal = $74$

$m = n \times M = 0.21763 \times 74 = 16.104\,\text{g}$

5. Round to nearest integer

$16.104 \approx 16\,\text{g}$

6. Final Answer

Required mass of 3-hydroxy propanal is:

$\boxed{16}$