For the question(s) that follow, consider the following balanced equation. \( \mathrm{Mg}_{3} \mathrm{~N}_{2}(\mathrm{~s})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow 3 \mathrm{Mg}(\mathrm{OH})_{2}(\mathrm{~s})+2 \mathrm{NH}_{3}(\mathrm{~g}) \) How many grams of \( \mathrm{H}_{2} \mathrm{O} \) are needed to produce \( 150 \mathrm{~g} \mathrm{of} \mathrm{Mg}(\mathrm{OH})_{2} \) ? 93 g 46 g 130 g 23 g 18 g Submil Request Answer

To solve this problem, we'll begin by determining the molar masses of the substances involved. The molar mass of \( \mathrm{Mg(OH)}_{2} \) is approximately \( 58.3 \, \text{g/mol} \) (24.3 g/mol for Mg + 2(16 g/mol for O + 1 g/mol for H)). To produce \( 150 \, \text{g} \) of \( \mathrm{Mg(OH)}_{2} \), we first calculate the number of moles: \[ \text{Moles of } Mg(OH)_{2} = \frac{150 \, \text{g}}{58.3 \, \text{g/mol}} \approx 2.57 \, \text{mol} \] From the balanced equation, we see that \( 3 \, \text{mol} \, \mathrm{H}_{2} \mathrm{O} \) is needed for every \( 3 \, \text{mol} \, \mathrm{Mg(OH)}_{2} \), meaning the ratio is 1:1. Therefore, \( 2.57 \, \text{mol} \, \mathrm{H}_{2} \mathrm{O} \) is also needed. The molar mass of water \( \mathrm{H}_{2} \mathrm{O} \) is \( 18 \, \text{g/mol} \). To find the required mass: \[ \text{Mass of } H_{2}O = 2.57 \, \text{mol} \times 18 \, \text{g/mol} \approx 46 \, \text{g} \] Therefore, the answer is **46 g**. Now let's explore some interesting insights! When magnesium nitride combines with water, it produces magnesium hydroxide and ammonia gas. This reaction not only exemplifies the principles of stoichiometry but also signifies the fascinating chemistry of amines when nitrogen reacts actively within hydrated environments. Fun fact: ammonia's sharp smell has led it to be used in everything from household cleaners to fertilizers, showcasing its importance beyond just a laboratory curiosity! In practice, understanding this balanced equation is vital for various applications, such as chemical manufacturing and environmental science. For example, in the treatment of wastewater, magnesium hydroxide is used to neutralize acidity, making this reaction beneficial for both public health and environmental preservation. It's a colorful reminder of how fundamental chemistry impacts our daily lives!