Q: A student measures the volume of hydrogen gas collected as $$90.0\ \mathrm{mL} at a $$pressure of $$0.9627\ \mathrm{atm}$$ and a temperature of $$297\ \mathrm{K}. $$Calculate the number of moles of hydrogen gas using the ideal gas law.

$$n = \frac{PV}{RT} = \frac{0.9627 \times 0.0900}{0.0821 \times 297} = 0.00357\ \mathrm{mol}$$

Q: If a student experimentally determines the ideal gas law constant $$R to be$$ $$0.08087\ \mathrm{L\cdot atm/(mol\cdot K)}$$ and the accepted value is $$0.0821\ \mathrm{L\cdot atm/(mol\cdot K)}$$, what is the percent error?

$$\frac{|0.08087 - 0.0821|}{0.0821} \times 100 = 1.50\%$$

Q: Given the densities: mercury $$= 13.6\ \mathrm{g/mL}$$, water $$= 1.00\ \mathrm{g/mL}$$, and a height difference of $$28.0\ \mathrm{cm} in $$water, what is the equivalent pressure difference in mm Hg?

$$\frac{1.00}{13.6} \times 28.0 \times 10 = 20.6\ \mathrm{mm\ Hg}$$

Question 1

In the experiment described, magnesium reacts with hydrochloric acid to produce hydrogen gas. What is the balanced molecular equation for this reaction?

Accepted Answer

$$\mathrm{Mg(s) + 2HCl(aq) \rightarrow $$MgCl_2$$(aq) + H_2$(g)}$$

Question 2

A student collects hydrogen gas over water at 25°C. The atmospheric pressure is 756.80 mm Hg, and the vapor pressure of water at 25°C is 22.31 mm Hg. What is the pressure of the dry hydrogen gas collected?

Accepted Answer

$$756.80\ \mathrm{mm\ Hg} - 22.31\ \mathrm{mm\ Hg} = 734.49\ \mathrm{mm\ Hg}$$

Question 3

Which of the following best describes Dalton's Law of Partial Pressures as applied in the experiment?

Accepted Answer

The total pressure of a gas mixture is the sum of the partial pressures of each individual gas present.

Question 4

A student measures the volume of hydrogen gas collected as $$90.0\ \mathrm{mL} at a $$pressure of $$0.9627\ \mathrm{atm}$$ and a temperature of $$297\ \mathrm{K}. $$Calculate the number of moles of hydrogen gas using the ideal gas law.

Accepted Answer

$$n = \frac{PV}{RT} = \frac{0.9627 	imes 0.0900}{0.0821 	imes 297} = 0.00357\ \mathrm{mol}$$

Question 5

If a student experimentally determines the ideal gas law constant $$R to be$$ $$0.08087\ \mathrm{L\cdot atm/(mol\cdot K)}$$ and the accepted value is $$0.0821\ \mathrm{L\cdot atm/(mol\cdot K)}$$, what is the percent error?

Accepted Answer

$$\frac{|0.08087 - 0.0821|}{0.0821} 	imes 100 = 1.50\%$$

Question 6

In the experiment, why is it necessary to subtract the vapor pressure of water from the total pressure when calculating the pressure of hydrogen gas collected over water?

Accepted Answer

Because the total pressure includes both hydrogen gas and water vapor, and only the pressure due to hydrogen gas is needed for calculations.

Question 7

A student neglects to account for the higher water level in the eudiometer compared to the beaker. How will this affect the calculated value of $$R$$?

Accepted Answer

The calculated value of $$R$$ will be too small because the actual pressure of hydrogen gas is lower than assumed.

Question 8

Given the densities: mercury $$= 13.6\ \mathrm{g/mL}$$, water $$= 1.00\ \mathrm{g/mL}$$, and a height difference of $$28.0\ \mathrm{cm} in $$water, what is the equivalent pressure difference in mm Hg?

Accepted Answer

$$\frac{1.00}{13.6} 	imes 28.0 	imes 10 = 20.6\ \mathrm{mm\ Hg}$$

Question 9

If some hydrogen gas escapes during the experiment, which of the following best describes the effect on the calculated moles of hydrogen and the value of $$R$$?

Accepted Answer

The calculated moles of hydrogen will be smaller than the actual value, causing the calculated $$R to be $$too large.

Question 10

Which of the following is the correct net ionic equation for the reaction between magnesium and hydrochloric acid?

Accepted Answer

$$\mathrm{Mg(s) + 2H^+(aq) \rightarrow Mg$$^{2+}$$(aq) + H_2$(g)}$$

Question 11

A student collects $$0.090\ \mathrm{g} of $$hydrogen gas. How many moles of hydrogen gas is this?

Accepted Answer

$$n = \frac{0.090}{2.02} = 0.0446\ \mathrm{mol}$$

Question 12

Why is it important to use a closed system when collecting hydrogen gas in this experiment?

Accepted Answer

To prevent the escape of hydrogen gas, ensuring accurate measurement of the volume produced.

Question 13

If the temperature of the gas is measured incorrectly and is actually higher than recorded, how will this affect the calculated value of $$R$$?

Accepted Answer

The calculated value of $$R$$ will be too small because $$T is in $$the denominator of $$R = \frac{PV}{nT}.$$

Question 14

Which of the following is a source of systematic error in the determination of the gas law constant $$R in $$this experiment?

Accepted Answer

Not accounting for the vapor pressure of water when calculating the pressure of hydrogen gas.

Question 15

A student uses $$0.090\ \mathrm{g} of $$magnesium in the reaction. How many moles of hydrogen gas should be produced, assuming complete reaction?

Accepted Answer

$$n = \frac{0.090}{24.305} = 0.00370\ \mathrm{mol}$$

Question 16

In the experiment, why is it necessary to measure the height difference between the water levels in the eudiometer and the beaker?

Accepted Answer

To account for the pressure difference due to the column of water, which affects the total pressure inside the eudiometer.

Question 17

If the vapor pressure of water is not subtracted from the total pressure, what is the likely effect on the calculated moles of hydrogen gas?

Accepted Answer

The calculated moles will be too large because the pressure used is higher than the actual pressure of hydrogen gas.

Question 18

Which of the following is the correct formula for calculating the pressure of hydrogen gas collected over water?

Accepted Answer

$$P_{\mathrm{H}_2$$} = P_{	ext{total}} - $$P_{	ext{H}_2O$$}$$

Determination of the Ideal Gas Law Constant (R) Using Hydrogen Gas Generation

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