Final answer:
To calculate the mass of liquid oxygen necessary for all the hydrogen to burn in the U.S. space shuttle's main engines, we need to use the balanced chemical equation for the combustion of hydrogen. Based on the equation, 2 moles of hydrogen react with 1 mole of oxygen to produce 2 moles of water. Given the mass of liquid hydrogen, we can calculate the mass of liquid oxygen needed using the molar ratio.
Step-by-step explanation:
The main engines of the U.S. space shuttle are powered by liquid hydrogen and liquid oxygen. In order to calculate the mass of liquid oxygen necessary for all the hydrogen to burn, we need to understand the balanced chemical equation for the combustion of hydrogen. The equation is:
2H2 + O2 → 2H2O
Based on the equation, we can see that 2 moles of hydrogen reacts with 1 mole of oxygen to produce 2 moles of water.
Given that there is 1.02×105 kg of liquid hydrogen, we need to convert this mass to moles by dividing it by the molar mass of hydrogen (2 g/mol). This gives us:
1.02×105 kg × (1000 g/kg) / (2 g/mol) = 5.1×107 mol of hydrogen
Since the ratio of hydrogen to oxygen is 2:1, we need half as many moles of oxygen as hydrogen. Therefore, the mass of liquid oxygen necessary for all the hydrogen to burn is:
5.1×107 mol × (32 g/mol) / (1000 g/kg) = 1.632×106 kg of oxygen.