Problem 39
Question
Determine the volume of hydrogen gas needed to react completely with 5.00 L of oxygen gas to form water.
Step-by-Step Solution
Verified Answer
10.00 L of hydrogen gas is needed.
1Step 1: Write the balanced chemical equation
To solve this problem, start by writing the balanced chemical equation for the reaction between hydrogen and oxygen to form water: \[ 2H_2(g) + O_2(g)
ightarrow 2H_2O(l) \] This equation tells us that 2 moles of hydrogen gas react with 1 mole of oxygen gas to produce water.
2Step 2: Understand the volume ratio from the equation
According to the balanced equation from Step 1, the ratio of hydrogen gas to oxygen gas is 2:1. This means that 2 volumes of hydrogen gas are needed to react with 1 volume of oxygen gas.
3Step 3: Calculate the volume of hydrogen gas needed
Since 2 volumes of hydrogen react with 1 volume of oxygen, if you have 5.00 L of oxygen gas, you need twice that volume in hydrogen gas: \[ \text{Volume of } H_2 = 2 \times 5.00 \, L = 10.00 \, L \] Therefore, 10.00 L of hydrogen gas is needed to react completely with 5.00 L of oxygen gas.
Key Concepts
Chemical EquationVolume RatioGas ReactionBalanced Equation
Chemical Equation
In chemistry, a chemical equation is a symbolic representation of a chemical reaction. It shows the reactants, which are the starting materials, and the products, which are the substances formed in the reaction. For the reaction of hydrogen (H_2) with oxygen (O_2) to form water (H_2O), the chemical equation is written as follows:\[ 2H_2(g) + O_2(g) \rightarrow 2H_2O(l) \]This equation provides vital information about the reaction. It indicates that two molecules of hydrogen gas react with one molecule of oxygen gas to produce two molecules of liquid water. In this equation, "g" stands for gas and "l" stands for liquid. The equation must be balanced, meaning the number of atoms of each element is the same on both sides.
Volume Ratio
The volume ratio in a chemical reaction is derived directly from the coefficients of the balanced equation. This is a crucial aspect of stoichiometry, which deals with the quantitative relationships between reactants and products in a chemical reaction. Based on our balanced chemical equation, the ratio of hydrogen gas (
H_2
) to oxygen gas (
O_2
) is 2:1.
This means that for every 1 volume of O_2 , we need 2 volumes of H_2 to completely react without leaving excess reactants. Therefore, if you have 5.00 liters of oxygen gas, you will need twice that amount, or 10.00 liters of hydrogen gas. Volume ratios are particularly useful when dealing with gases because gas volumes can be easily measured under the same conditions of temperature and pressure.
This means that for every 1 volume of O_2 , we need 2 volumes of H_2 to completely react without leaving excess reactants. Therefore, if you have 5.00 liters of oxygen gas, you will need twice that amount, or 10.00 liters of hydrogen gas. Volume ratios are particularly useful when dealing with gases because gas volumes can be easily measured under the same conditions of temperature and pressure.
Gas Reaction
Gas reactions involve the interaction of gases under specific conditions to form new substances. Often, these reactions require balancing as both the type and number of atoms must be conserved. For gases, this is performed using Avogadro’s Law, which states that equal volumes of gases at the same temperature and pressure contain an equal number of particles.
In the reaction between hydrogen gas and oxygen gas, both reactants are in the gaseous state and they form water, comprising diatomic molecules combining to form a compound. Under the principles of stoichiometry, we can directly relate the volume of gas consumed or produced to the number of moles reacting, given a constant temperature and pressure. This makes calculations straightforward when predicting the volumes of gases involved.
In the reaction between hydrogen gas and oxygen gas, both reactants are in the gaseous state and they form water, comprising diatomic molecules combining to form a compound. Under the principles of stoichiometry, we can directly relate the volume of gas consumed or produced to the number of moles reacting, given a constant temperature and pressure. This makes calculations straightforward when predicting the volumes of gases involved.
Balanced Equation
A balanced equation is fundamental in chemical reactions as it ensures the law of conservation of mass is maintained; that is, matter is neither created nor destroyed. To balance an equation, adjust the coefficients (numbers in front of atoms or molecules) so that the number of atoms for each element is equal on both sides of the reaction.
Consider the equation for forming water:\[ 2H_2(g) + O_2(g) \rightarrow 2H_2O(l) \]This equation is balanced because:
Consider the equation for forming water:\[ 2H_2(g) + O_2(g) \rightarrow 2H_2O(l) \]This equation is balanced because:
- The number of hydrogen atoms: 4 (2 × 2 in H_2) on the left equals 4 in the two water molecules on the right.
- The number of oxygen atoms: 2 in O_2 on the left equals 2 in the water molecules on the right.
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