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Answer :
Sure, let's work through this problem step by step.
To find the mass of 0.10 mol of [tex]\( KHC_4H_4O_6 \)[/tex], we need to calculate its molar mass first. A compound's molar mass is the sum of the atomic masses of all the atoms in a molecule.
### Step 1: Identify the atomic masses
- Potassium (K): 39.10 g/mol
- Hydrogen (H): 1.01 g/mol
- Carbon (C): 12.01 g/mol
- Oxygen (O): 16.00 g/mol
### Step 2: Calculate the molar mass of [tex]\( KHC_4H_4O_6 \)[/tex]
The molecular formula [tex]\( KHC_4H_4O_6 \)[/tex] tells us that it contains:
- 1 Potassium atom
- 5 Hydrogen atoms (1 from KHC and 4 from C4H4)
- 4 Carbon atoms
- 6 Oxygen atoms
Now, let's compute the molar mass:
1. Potassium: [tex]\( 1 \times 39.10 \)[/tex] = 39.10 g/mol
2. Hydrogen: [tex]\( 5 \times 1.01 \)[/tex] = 5.05 g/mol
3. Carbon: [tex]\( 4 \times 12.01 \)[/tex] = 48.04 g/mol
4. Oxygen: [tex]\( 6 \times 16.00 \)[/tex] = 96.00 g/mol
Add these up to get the total molar mass:
[tex]\[ 39.10 + 5.05 + 48.04 + 96.00 = 188.19 \, \text{g/mol} \][/tex]
### Step 3: Calculate the mass of 0.10 mol of [tex]\( KHC_4H_4O_6 \)[/tex]
The formula to calculate mass is:
[tex]\[ \text{Mass} = \text{Moles} \times \text{Molar Mass} \][/tex]
Given:
- Moles = 0.10 mol
- Molar Mass = 188.19 g/mol
So, the mass is:
[tex]\[ 0.10 \, \text{mol} \times 188.19 \, \text{g/mol} = 18.819 \, \text{g} \][/tex]
Thus, the mass found in 0.10 mol of [tex]\( KHC_4H_4O_6 \)[/tex] is approximately 19 g. The correct answer choice is (b) 19 g.
To find the mass of 0.10 mol of [tex]\( KHC_4H_4O_6 \)[/tex], we need to calculate its molar mass first. A compound's molar mass is the sum of the atomic masses of all the atoms in a molecule.
### Step 1: Identify the atomic masses
- Potassium (K): 39.10 g/mol
- Hydrogen (H): 1.01 g/mol
- Carbon (C): 12.01 g/mol
- Oxygen (O): 16.00 g/mol
### Step 2: Calculate the molar mass of [tex]\( KHC_4H_4O_6 \)[/tex]
The molecular formula [tex]\( KHC_4H_4O_6 \)[/tex] tells us that it contains:
- 1 Potassium atom
- 5 Hydrogen atoms (1 from KHC and 4 from C4H4)
- 4 Carbon atoms
- 6 Oxygen atoms
Now, let's compute the molar mass:
1. Potassium: [tex]\( 1 \times 39.10 \)[/tex] = 39.10 g/mol
2. Hydrogen: [tex]\( 5 \times 1.01 \)[/tex] = 5.05 g/mol
3. Carbon: [tex]\( 4 \times 12.01 \)[/tex] = 48.04 g/mol
4. Oxygen: [tex]\( 6 \times 16.00 \)[/tex] = 96.00 g/mol
Add these up to get the total molar mass:
[tex]\[ 39.10 + 5.05 + 48.04 + 96.00 = 188.19 \, \text{g/mol} \][/tex]
### Step 3: Calculate the mass of 0.10 mol of [tex]\( KHC_4H_4O_6 \)[/tex]
The formula to calculate mass is:
[tex]\[ \text{Mass} = \text{Moles} \times \text{Molar Mass} \][/tex]
Given:
- Moles = 0.10 mol
- Molar Mass = 188.19 g/mol
So, the mass is:
[tex]\[ 0.10 \, \text{mol} \times 188.19 \, \text{g/mol} = 18.819 \, \text{g} \][/tex]
Thus, the mass found in 0.10 mol of [tex]\( KHC_4H_4O_6 \)[/tex] is approximately 19 g. The correct answer choice is (b) 19 g.
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