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There is a balloon filled with 1 liter of methane, CH_(4) gas at STP and a balloon filled with one liter of hydrogen gas, H_(2) at STP, which balloon contains more grams of hydrogen gas? CH_(4) They are equal H_(2) Not enough information

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There is a balloon filled with 1 liter of methane, CH_(4) gas at STP and a balloon filled with one
liter of hydrogen gas, H_(2) at STP, which balloon contains more grams of hydrogen gas?
CH_(4)
They are equal
H_(2)
Not enough information

There is a balloon filled with 1 liter of methane, CH_(4) gas at STP and a balloon filled with one liter of hydrogen gas, H_(2) at STP, which balloon contains more grams of hydrogen gas? CH_(4) They are equal H_(2) Not enough information

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KirkMaster · Tutor for 5 years

Answer

### C. \( \mathrm{H}_{2} \)

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## Step 1: Understand STP conditions and molar volume<br />At standard temperature and pressure (STP - 0°C and 1 atm), 1 mole of any ideal gas occupies 22.4 liters.<br /><br />## Step 2: Calculate molar mass of gases<br />- Molar mass of \( \mathrm{CH}_{4} \): \( \mathrm{C} = 12.01 \, \mathrm{g/mol}, \ \mathrm{H} = 1.01 \, \mathrm{g/mol} \)<br />\[ Molar \ mass \ of \ \mathrm{CH}_{4} = 12.01 + 4 \times 1.01 = 16.05 \, \mathrm{g/mol} \]<br />- Molar mass of \( \mathrm{H}_{2} \): <br />\[ Molar \ mass \ of \ \mathrm{H}_{2} = 2 \times 1.01 = 2.02 \, \mathrm{g/mol} \]<br /><br />## Step 3: Determine moles in 1 liter<br />Given that 22.4 liters of gas equals 1 mole at STP:<br />\[ Moles \ in \ 1 \ liter = \frac{1 \ \mathrm{liter}}{22.4 \ \mathrm{liters/mol}} = 0.04464 \ \mathrm{moles} \]<br /><br />## Step 4: Calculate mass of gases in 1 liter<br />- Mass of \( \mathrm{CH}_{4} \):<br />\[ 0.04464 \ \mathrm{moles} \times 16.05 \ \mathrm{g/mol} = 0.716 \ \mathrm{g} \]<br />- Mass of \( \mathrm{H}_{2} \):<br />\[ 0.04464 \ \mathrm{moles} \times 2.02 \ \mathrm{g/mol} = 0.090 \ \mathrm{g} \]<br /><br />## Step 5: Compare masses of gases<br />Comparing 0.716 grams of methane to 0.090 grams of hydrogen:<br />\[ \mathrm{CH}_{4} > \mathrm{H}_{2} \]
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