May be solved by the molar volume method (Section 14.7 ) or...

May be solved by the molar volume method (Section 14.7 ) or by the ideal gas equation method (Section 14.8 ). In the answer section, the setups are given first for the molar volume method, printed over a tan background. Then, over a green back- ground, the answers are given for the ideal gas equation method. Check your work according to the section you studied. How many grams of sodium are needed to produce $25.3 \mathrm{L}$ of hydrogen gas at $43^{\circ} \mathrm{C}$ and 0.886 atm according to the reaction $2 \mathrm{Na}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow 2 \mathrm{NaOH}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{g}) ?$

May be solved by the molar volume method (Section 14.7 ) or by the ideal gas equation method (Section 14.8 ). In the answer section, the setups are given first for the molar volume method, printed over a tan background. Then, over a green back-
ground, the answers are given for the ideal gas equation method. Check your work according to the section you studied.
How many grams of sodium are needed to produce $25.3 \mathrm{L}$ of hydrogen gas at $43^{\circ} \mathrm{C}$ and 0.886 atm according to the reaction $2 \mathrm{Na}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow 2 \mathrm{NaOH}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{g}) ?$

Key Concepts

Chemical Reaction Stoichiometry

This concept involves using the balanced chemical equation to determine the quantitative relationships between reactants and products. By applying stoichiometry, one calculates the moles of a reactant or product needed or formed based on the mole ratios provided in the balanced equation.

Ideal Gas Equation (PV = nRT)

The ideal gas law is a fundamental equation relating the pressure, volume, temperature, and number of moles of a gas. It is used to determine the number of moles present under non-standard conditions by rearranging the equation to solve for n, highlighting the dependence of a gas’s volume on both its pressure and temperature.

Molar Volume Concept

The molar volume method involves using the volume occupied by one mole of a gas under specified conditions, often standard temperature and pressure, to calculate the number of moles present in a given volume of gas. This approach simplifies gas stoichiometry when working with known molar volumes.

Unit Conversion

Accurate problem solving in gas stoichiometry requires careful conversion of units, especially converting temperature from Celsius to Kelvin and ensuring pressure and volume are expressed in consistent units. Proper unit conversion is critical for correctly applying equations like the ideal gas law.

Transcript

00:02 Hi there and welcome.

00:04 In this problem, i want to start out by writing the balanced equation that we are provided with in the problem.

00:11 It's 2na plus 2h2o produces 2naoh and hydrogen gas.

00:41 What we want to know is we want to know how many grams of the sodium we need to start with to produce 25 .3 liters.

00:54 Of this hydrogen gas.

00:58 However, the hydrogen gas is not at stp.

01:01 Instead, it's at 43 degrees celsius and 0 .886 atmospheres.

01:14 I'm going to go ahead and convert this temperature to kelvin right away by adding 273, and that gives me 316 kelvin.

01:31 All right.

01:32 So let's think about this problem.

01:35 Noticing that i am trying to find out information about a reactant when i have information about one of the products tells me i'm going to have to do some stoichiometry.

01:47 But before i can do that, i need to figure out how many moles of that hydrogen i'm trying to make.

01:54 I have volume, but i need to know how many moles.

01:57 And i can't simply use 22 .4 to tell me that because i am not at stp.

02:03 What i am going to have to use is the ideal gas equation.

02:09 And when i rearrange that for a number of moles, i get n equals pv over rt.

02:18 So i can calculate the moles of hydrogen that i have from this equation and the information that was given.

02:25 Let's go ahead and do that.

02:28 Pressure is 0 .86 atmospheres.

02:36 The volume that we are given in this problem is 25 .3 liters.

02:46 The universal gas constant that i would like to use is the one that has atmospheres in it, since my pressure is in atmospheres.

03:04 And then i need to multiply down here by my temperature, which is in kelvin at 316.

03:13 316 kelvin.

03:16 I'm going to quick check of units here...

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