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The salt [tex]$BeC_2O_4(s)$[/tex] forms a hydrate. When heated to [tex]$220^{\circ} C$[/tex], the salt dehydrates as follows:

[tex]\[BeC_2O_4 \cdot 3 H_2O (s) \rightarrow BeC_2O_4 (s) + 3 H_2O (g)\][/tex]

Answer the following questions about [tex]$BeC_2O_4(s)$[/tex] and its hydrate:

1. Define the term "hydrate."
2. Calculate the mass percent of carbon in the hydrated form of the solid, which has the formula [tex]$BeC_2O_4 \cdot 3 H_2O$[/tex].

Sagot :

GinnyAnsweridn
A hydrate is a compound that contains water molecules bound to another compound or an element. These water molecules are incorporated into the crystalline structure of the compound.

Given the hydrated salt with the formula [tex]\( BeC_2O_4 \cdot 3H_2O \)[/tex], let's determine the mass percent of carbon in this hydrated form. We need to perform several steps to find this value:

1. Determine the atomic masses of each element in the compound:
- Hydrogen (H): 1.008 g/mol
- Oxygen (O): 16.00 g/mol
- Carbon (C): 12.01 g/mol
- Beryllium (Be): 9.012 g/mol

2. Calculate the molar mass of the hydrated compound [tex]\( BeC_2O_4 \cdot 3H_2O \)[/tex]:
- Molar mass of [tex]\( BeC_2O_4 \)[/tex]:
- Beryllium (Be): [tex]\( 1 \times 9.012 \)[/tex] g/mol
- Carbon (C): [tex]\( 2 \times 12.01 \)[/tex] g/mol
- Oxygen (O): [tex]\( 4 \times 16.00 \)[/tex] g/mol
- Molar mass of [tex]\( BeC_2O_4 \)[/tex]:

[tex]\[ 9.012 + 2 \times 12.01 + 4 \times 16.00 = 9.012 + 24.02 + 64.00 = 97.032 \ \text{g/mol} \][/tex]

- Molar mass of [tex]\( 3H_2O \)[/tex]:
- Hydrogen (H): [tex]\( 3 \times 2 \times 1.008 \)[/tex] g/mol
- Oxygen (O): [tex]\( 3 \times 16.00 \)[/tex] g/mol
- Molar mass of [tex]\( 3H_2O \)[/tex]:

[tex]\[ 3 \times (2 \times 1.008) + 3 \times 16.00 = 3 \times 2.016 + 48.00 = 6.048 + 48.00 = 54.048 \ \text{g/mol} \][/tex]

- Total molar mass of [tex]\( BeC_2O_4 \cdot 3H_2O \)[/tex]:

[tex]\[ 97.032 + 54.048 = 151.08 \ \text{g/mol} \][/tex]

3. Calculate the mass of carbon atoms in the hydrated compound:
- Number of carbon atoms in [tex]\( BeC_2O_4 \cdot 3H_2O \)[/tex]: 2
- Mass of carbon atoms:

[tex]\[ 2 \times 12.01 = 24.02 \ \text{g/mol} \][/tex]

4. Calculate the mass percent of carbon in [tex]\( BeC_2O_4 \cdot 3H_2O \)[/tex]:
- Mass percent of carbon:

[tex]\[ \frac{\text{Mass of Carbon}}{\text{Molar Mass of Hydrate}} \times 100 = \frac{24.02}{151.08} \times 100 \approx 15.90\% \][/tex]

Therefore, the mass percent of carbon in the hydrated form of the solid [tex]\( BeC_2O_4 \cdot 3H_2O \)[/tex] is approximately [tex]\( 15.90\% \)[/tex].
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