A deep-sea diver uses a gas cylinder with a volume of 10.0 L and a content of 51.2 g of O2 and 32.6 g of He. Calculate the partial pressure of each gas and the total pressure if the temperature of the gas is 19 °C.

Verified step by step guidance

1. Step 1: Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature. This is necessary because gas law calculations require temperature in Kelvin.
2. Step 2: Calculate the number of moles of each gas using the formula \( n = \frac{m}{M} \), where \( n \) is the number of moles, \( m \) is the mass of the gas, and \( M \) is the molar mass of the gas. Use the molar mass of O2 (32.00 g/mol) and He (4.00 g/mol).
3. Step 3: Use the ideal gas law \( PV = nRT \) to calculate the partial pressure of each gas. Rearrange the formula to \( P = \frac{nRT}{V} \), where \( P \) is the pressure, \( n \) is the number of moles, \( R \) is the ideal gas constant (0.0821 L·atm/mol·K), \( T \) is the temperature in Kelvin, and \( V \) is the volume in liters.
4. Step 4: Calculate the partial pressure of O2 by substituting the number of moles of O2, the ideal gas constant, the temperature in Kelvin, and the volume of the cylinder into the rearranged ideal gas law equation.
5. Step 5: Calculate the partial pressure of He using the same method as in Step 4, substituting the number of moles of He. Then, add the partial pressures of O2 and He to find the total pressure in the gas cylinder.