CH3 OH can be synthesized by the reaction: CO(g)+2 H2(g) ⟶CH3 OH(g) How many liters of H2 gas, m

CH3 OH can be synthesized by the reaction: CO(g)+2 H2(g)...

$\mathrm{CH}_{3} \mathrm{OH}$ can be synthesized by the reaction: $$ \mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(g) $$ How many liters of $\mathrm{H}_{2}$ gas, measured at $748 \mathrm{mm} \mathrm{Hg}$ and $86^{\circ} \mathrm{C},$ are required to synthesize $0.55 \mathrm{mol}$ of $\mathrm{CH}_{3} \mathrm{OH} ? \mathrm{How}$ many liters of CO gas, measured under the same conditions, are required?

$\mathrm{CH}_{3} \mathrm{OH}$ can be synthesized by the reaction:
$$
\mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(g)
$$
How many liters of $\mathrm{H}_{2}$ gas, measured at $748 \mathrm{mm} \mathrm{Hg}$ and $86^{\circ} \mathrm{C},$ are required to synthesize $0.55 \mathrm{mol}$ of $\mathrm{CH}_{3} \mathrm{OH} ? \mathrm{How}$
many liters of CO gas, measured under the same conditions, are required?

Key Concepts

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, relates the pressure (P), volume (V), number of moles (n), and temperature (T) of a gas through the gas constant (R). This equation is crucial for converting between moles and volume under various conditions of temperature and pressure, allowing accurate calculations of the volumes of gases involved in chemical reactions, especially under non-standard conditions.

Balanced Chemical Equations and Stoichiometry

This concept involves using a balanced chemical equation to relate the proportions of reactants and products in a chemical reaction. Stoichiometry provides the quantitative relationships between reactants and products, enabling calculation of the amount of one substance required or produced based on the known amount of another. It is essential for determining how many moles of a reagent are needed to synthesize a given number of moles of product.

Transcript

00:03 In this problem, we have carbon monoxide and hydrogen gas reacting to form methanol, and we're asked how many liters of hydrogen gas at 748 millimeters of mercury, 86 degrees celsius, do we need to form 0 .55 moles of methanol? and then how many liters of carbon monoxide gas measured under the same conditions would be required? so the first thing i'm going to do is convert everything into the correct units.

00:37 We're going to be using the ideal gas equation to solve for volume here.

00:41 So we need to have everything in the right units for that.

00:44 So pressure needs to be in atmospheres.

00:46 So we'll take that 748 millimeters of mercury.

00:53 And then one atmosphere is equal to 760 millimeters of mercury.

00:59 So we can cancel out these units.

01:01 And that gives us 0 .984 atmospheres is our pressure.

01:08 And then for temperature, that needs to be in kelvin.

01:10 So to get to kelvin from celsius, you just add 273.

01:15 So 86 plus 273 gives me 359 kelvin.

01:22 So these are the values i'm going to be using.

01:25 So the first thing i'm going to do is find the volume, or sorry, we're looking for the volume of hydrogen gas that would be needed to make 0 .55 moles of methanol.

01:42 So i'm first going to convert this 0 .55 moles of methanol.

01:46 It's moles of hydrogen.

01:47 So 0 .55 moles of, whoops, methanol is, so for one mole of methanol, we need two moles of hydrogen, two, what am i doing? two moles of hydrogen per one mole of methanol.

02:12 So if i do that math really quick, that'll give me 1 .1 moles of hydrogen.

02:20 Hydrogen gas.

02:21 So now i can use all these conditions i've been given to calculate the volume of this 1 .1 moles of hydrogen gas.

02:28 So p b equals nr t.

02:31 This is the ideal gas equation.

02:33 That's what we're going to be using to calculate the volume.

02:35 P is pressure, which we found over here, and is the number of moles, which we just solved for...

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