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QuestionWhen 10.7 g10.7 \mathrm{~g} of marble reacts with 60.3 mL60.3 \mathrm{~mL} HCl, how many liters of CO2_2 gas are produced? Density of CO2_2 is 1.798 g/L1.798 \mathrm{~g} / \mathrm{L}.

Studdy Solution

STEP 1

Assumptions1. The initial weight of marble chips is 10.7 g10.7 \mathrm{~g} . The volume of hydrochloric acid used is 60.3 m60.3 \mathrm{~m} with a density of 1.096 g/m1.096 \mathrm{~g} / \mathrm{m}
3. The final weight of the solution is 72.1 g72.1 \mathrm{~g}
4. The density of carbon dioxide gas is 1.798 g/1.798 \mathrm{~g} / \mathrm{}

STEP 2

First, we need to find the weight of the hydrochloric acid. We can do this by multiplying the volume of the acid by its density.
WeightHCl=VolumeHCltimesDensityHClWeight_{HCl} = Volume_{HCl} \\times Density_{HCl}

STEP 3

Now, plug in the given values for the volume and density of the hydrochloric acid to calculate its weight.
WeightHCl=60.3 mtimes1.096 g/mWeight_{HCl} =60.3 \mathrm{~m} \\times1.096 \mathrm{~g} / \mathrm{m}

STEP 4

Calculate the weight of the hydrochloric acid.
WeightHCl=60.3 mtimes1.096 g/m=66.1 gWeight_{HCl} =60.3 \mathrm{~m} \\times1.096 \mathrm{~g} / \mathrm{m} =66.1 \mathrm{~g}

STEP 5

Now, we can find the total initial weight before the reaction. This includes both the weight of the marble chips and the weight of the hydrochloric acid.
Weightinitial=Weightmarble+WeightHClWeight_{initial} = Weight_{marble} + Weight_{HCl}

STEP 6

Plug in the values for the weight of the marble chips and the weight of the hydrochloric acid to calculate the initial weight.
Weightinitial=10. g+66.1 gWeight_{initial} =10. \mathrm{~g} +66.1 \mathrm{~g}

STEP 7

Calculate the initial weight before the reaction.
Weightinitial=10.7 g+66.1 g=76. gWeight_{initial} =10.7 \mathrm{~g} +66.1 \mathrm{~g} =76. \mathrm{~g}

STEP 8

The weight of the carbon dioxide gas released can be found by subtracting the final weight of the solution from the initial weight before the reaction.
WeightCO2=Weightinitial−WeightfinalWeight_{CO2} = Weight_{initial} - Weight_{final}

STEP 9

Plug in the values for the initial weight and the final weight to calculate the weight of the carbon dioxide gas.
WeightCO2=76.8 g−72. gWeight_{CO2} =76.8 \mathrm{~g} -72. \mathrm{~g}

STEP 10

Calculate the weight of the carbon dioxide gas.
WeightCO2=76.8 g−72. g=4.7 gWeight_{CO2} =76.8 \mathrm{~g} -72. \mathrm{~g} =4.7 \mathrm{~g}

STEP 11

Now that we have the weight of the carbon dioxide gas, we can find the volume of the gas by dividing the weight of the gas by its density.
VolumeCO=WeightCO/DensityCOVolume_{CO} = Weight_{CO} / Density_{CO}

STEP 12

Plug in the values for the weight of the carbon dioxide gas and the density of the gas to calculate the volume of the gas.
VolumeCO2=4.7 g/.798 g/Volume_{CO2} =4.7 \mathrm{~g} /.798 \mathrm{~g} / \mathrm{}

STEP 13

Calculate the volume of the carbon dioxide gas.
VolumeCO2=.7 g/.798 g/=2.61 Volume_{CO2} =.7 \mathrm{~g} /.798 \mathrm{~g} / \mathrm{} =2.61 \mathrm{~}The volume of the carbon dioxide gas released is2.61 liters.

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