To calculate the total pressure in a mixture of 4 g of oxygen and 2 g of hydrogen confined in a total volume of 1 L at 0°C, we will use the ideal gas equation, which is given by:
\[ PV = nRT \]
Where:
- \( P \) = pressure (in atm)
- \( V \) = volume (in L)
- \( n \) = number of moles of gas
- \( R \) = ideal gas constant (0.0821 L·atm/(K·mol))
- \( T \) = temperature (in K)
### Step 1: Convert the temperature to Kelvin
The temperature is given as 0°C. To convert this to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273.15 \]
So,
\[ T = 0 + 273.15 = 273.15 \, K \]
### Step 2: Calculate the number of moles of oxygen (O₂)
The molar mass of oxygen (O₂) is approximately 32 g/mol. The number of moles of oxygen can be calculated using the formula:
\[ n = \frac{\text{mass}}{\text{molar mass}} \]
For oxygen:
\[ n_{O_2} = \frac{4 \, g}{32 \, g/mol} = 0.125 \, mol \]
### Step 3: Calculate the number of moles of hydrogen (H₂)
The molar mass of hydrogen (H₂) is approximately 2 g/mol. The number of moles of hydrogen can be calculated similarly:
\[ n_{H_2} = \frac{2 \, g}{2 \, g/mol} = 1 \, mol \]
### Step 4: Calculate the total number of moles in the mixture
The total number of moles \( n_{total} \) is the sum of the moles of oxygen and hydrogen:
\[ n_{total} = n_{O_2} + n_{H_2} = 0.125 \, mol + 1 \, mol = 1.125 \, mol \]
### Step 5: Use the ideal gas equation to calculate the pressure
Now we can substitute the values into the ideal gas equation to find the pressure \( P \):
\[ P = \frac{nRT}{V} \]
Substituting the values:
- \( n = 1.125 \, mol \)
- \( R = 0.0821 \, L·atm/(K·mol) \)
- \( T = 273.15 \, K \)
- \( V = 1 \, L \)
\[ P = \frac{(1.125 \, mol)(0.0821 \, L·atm/(K·mol))(273.15 \, K)}{1 \, L} \]
Calculating this gives:
\[ P = \frac{(1.125)(0.0821)(273.15)}{1} \approx 25.215 \, atm \]
### Final Answer
The total pressure in the mixture is approximately **25.215 atm**.
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