### Question 9: How many grams of ammonium chloride will dissolve in 50 grams of water at 45 °C?
The solubility of ammonium chloride (NH₄Cl) in water at 45 °C is given as 45 grams per 100 grams of water.
To calculate how many grams of ammonium chloride will dissolve in 50 grams of water, follow these steps:
1. Understand the ratio:
- Solubility = 45 grams of NH₄Cl per 100 grams of water
2. Set up the proportion:
- If 45 grams of NH₄Cl dissolve in 100 grams of water, then how many grams (denote it as [tex]\( x \)[/tex]) will dissolve in 50 grams of water?
[tex]\[
\frac{45 \text{ grams NH₄Cl}}{100 \text{ grams water}} = \frac{x \text{ grams NH₄Cl}}{50 \text{ grams water}}
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
- Cross-multiply to get:
[tex]\[
45 \times 50 = 100 \times x
\][/tex]
- Simplify:
[tex]\[
2250 = 100x
\][/tex]
- Divide by 100:
[tex]\[
x = 2250 / 100 = 22.5
\][/tex]
So, 22.5 grams of ammonium chloride will dissolve in 50 grams of water at 45 °C.
### Question 10: Calculate the mass of sodium nitrate that will dissolve in 50 grams of water at 20 °C.
The solubility of sodium nitrate (NaNO₃) in water at 20 °C is given as 88 grams per 100 grams of water.
To calculate how many grams of sodium nitrate will dissolve in 50 grams of water, follow these steps:
1. Understand the ratio:
- Solubility = 88 grams of NaNO₃ per 100 grams of water
2. Set up the proportion:
- If 88 grams of NaNO₃ dissolve in 100 grams of water, then how many grams (denote it as [tex]\( y \)[/tex]) will dissolve in 50 grams of water?
[tex]\[
\frac{88 \text{ grams NaNO₃}}{100 \text{ grams water}} = \frac{y \text{ grams NaNO₃}}{50 \text{ grams water}}
\][/tex]
3. Solve for [tex]\( y \)[/tex]:
- Cross-multiply to get:
[tex]\[
88 \times 50 = 100 \times y
\][/tex]
- Simplify:
[tex]\[
4400 = 100y
\][/tex]
- Divide by 100:
[tex]\[
y = 4400 / 100 = 44
\][/tex]
So, 44 grams of sodium nitrate will dissolve in 50 grams of water at 20 °C.
