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Sagot :
Let's solve the given problem step by step.
### 1. Writing the Balanced Chemical Equation
The reaction between calcium (Ca) and sulfuric acid (H₂SO₄) can be represented by the following balanced chemical equation:
[tex]\[ \text{Ca} + \text{H}_{2}\text{SO}_{4} \rightarrow \text{CaSO}_{4} + \text{H}_{2} \][/tex]
### 2. Calculate the Number of Moles of Calcium (Ca)
To begin with, we need to find the number of moles of calcium that react. The atomic mass of calcium (Ca) is given as 40 g/mol. Given that we start with 300 grams of calcium, we calculate the moles of Ca using the formula:
[tex]\[ \text{moles of Ca} = \frac{\text{mass of Ca}}{\text{molar mass of Ca}} \][/tex]
Substituting the values:
[tex]\[ \text{moles of Ca} = \frac{300 \text{ g}}{40 \text{ g/mol}} = 7.5 \text{ mol} \][/tex]
### 3. Calculate the Mass of Calcium Sulfate (CaSO₄) Formed
To find the mass of calcium sulfate formed, we first need to determine its molar mass. The molar mass of CaSO₄ is calculated by adding the atomic masses of its constituent elements:
[tex]\[ \text{Molar mass of CaSO}_{4} = 40 \ (\text{Ca}) + 32\ (\text{S}) + 4 \times 16 \ (\text{O}) = 136 \ \text{g/mol} \][/tex]
Using the moles of Ca calculated previously, we find the mass of CaSO₄ formed:
[tex]\[ \text{mass of CaSO}_{4} = \text{moles of Ca} \times \text{molar mass of CaSO}_{4} \][/tex]
[tex]\[ \text{mass of CaSO}_{4} = 7.5 \text{ mol} \times 136 \text{ g/mol} = 1020 \text{ g} \][/tex]
### 4. Calculate the Volume of Hydrogen Gas (H₂) Produced
At standard temperature and pressure (STP), one mole of gas occupies 22.4 liters. Using the moles of Ca from the reaction (since the reaction produces one mole of H₂ for each mole of Ca), we can calculate the volume of H₂ gas produced:
[tex]\[ \text{volume of H}_{2} = \text{moles of Ca} \times 22.4 \text{ L/mol} \][/tex]
[tex]\[ \text{volume of H}_{2} = 7.5 \text{ mol} \times 22.4 \text{ L/mol} = 168.0 \text{ L} \][/tex]
### Summary
Let's summarize the answers to the given problem:
1. The balanced equation for the reaction is:
[tex]\[ \text{Ca} + \text{H}_{2}\text{SO}_{4} \rightarrow \text{CaSO}_{4} + \text{H}_{2} \][/tex]
2. Calculation results:
- Number of moles of calcium (Ca) employed: 7.5 mol
- Mass of the compound (CaSO₄) formed: 1020 g
- Volume of hydrogen gas (H₂) produced: 168.0 L
### 1. Writing the Balanced Chemical Equation
The reaction between calcium (Ca) and sulfuric acid (H₂SO₄) can be represented by the following balanced chemical equation:
[tex]\[ \text{Ca} + \text{H}_{2}\text{SO}_{4} \rightarrow \text{CaSO}_{4} + \text{H}_{2} \][/tex]
### 2. Calculate the Number of Moles of Calcium (Ca)
To begin with, we need to find the number of moles of calcium that react. The atomic mass of calcium (Ca) is given as 40 g/mol. Given that we start with 300 grams of calcium, we calculate the moles of Ca using the formula:
[tex]\[ \text{moles of Ca} = \frac{\text{mass of Ca}}{\text{molar mass of Ca}} \][/tex]
Substituting the values:
[tex]\[ \text{moles of Ca} = \frac{300 \text{ g}}{40 \text{ g/mol}} = 7.5 \text{ mol} \][/tex]
### 3. Calculate the Mass of Calcium Sulfate (CaSO₄) Formed
To find the mass of calcium sulfate formed, we first need to determine its molar mass. The molar mass of CaSO₄ is calculated by adding the atomic masses of its constituent elements:
[tex]\[ \text{Molar mass of CaSO}_{4} = 40 \ (\text{Ca}) + 32\ (\text{S}) + 4 \times 16 \ (\text{O}) = 136 \ \text{g/mol} \][/tex]
Using the moles of Ca calculated previously, we find the mass of CaSO₄ formed:
[tex]\[ \text{mass of CaSO}_{4} = \text{moles of Ca} \times \text{molar mass of CaSO}_{4} \][/tex]
[tex]\[ \text{mass of CaSO}_{4} = 7.5 \text{ mol} \times 136 \text{ g/mol} = 1020 \text{ g} \][/tex]
### 4. Calculate the Volume of Hydrogen Gas (H₂) Produced
At standard temperature and pressure (STP), one mole of gas occupies 22.4 liters. Using the moles of Ca from the reaction (since the reaction produces one mole of H₂ for each mole of Ca), we can calculate the volume of H₂ gas produced:
[tex]\[ \text{volume of H}_{2} = \text{moles of Ca} \times 22.4 \text{ L/mol} \][/tex]
[tex]\[ \text{volume of H}_{2} = 7.5 \text{ mol} \times 22.4 \text{ L/mol} = 168.0 \text{ L} \][/tex]
### Summary
Let's summarize the answers to the given problem:
1. The balanced equation for the reaction is:
[tex]\[ \text{Ca} + \text{H}_{2}\text{SO}_{4} \rightarrow \text{CaSO}_{4} + \text{H}_{2} \][/tex]
2. Calculation results:
- Number of moles of calcium (Ca) employed: 7.5 mol
- Mass of the compound (CaSO₄) formed: 1020 g
- Volume of hydrogen gas (H₂) produced: 168.0 L
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