chemistry—unit 2 worksheet 3
problems 1 and 2. calculate the pressure of the gas in the flask connected to the manometer.
1.
a. proom = 730 mmhg diagram with p=, 84, 127
b. diagram with p=, 26, 130
c. diagram with p=, 95, 95
2.
proom : 733 mmhg
a. diagram with p=, 95, 41
b. diagram with p=, 104, 31
c. diagram with p=, 96, 138
3. what do we mean by atmospheric pressure? what causes this pressure?
4. how do we measure atmospheric pressure? is atmospheric pressure the same everywhere on the surface of the earth?

Question

chemistry—unit 2 worksheet 3
problems 1 and 2. calculate the pressure of the gas in the flask connected to the manometer.
1.
   a. proom = 730 mmhg diagram with p=, 84, 127
   b. diagram with p=, 26, 130
   c. diagram with p=, 95, 95
2.
   proom : 733 mmhg
   a. diagram with p=, 95, 41
   b. diagram with p=, 104, 31
   c. diagram with p=, 96, 138
3. what do we mean by atmospheric pressure? what causes this pressure?
4. how do we measure atmospheric pressure? is atmospheric pressure the same everywhere on the surface of the earth?

Accepted Answer

### Problem 1a:
# Explanation:
## Step1: Identify pressure relation (gas pressure + difference = room pressure? No, here gas pressure is less? Wait, manometer: if the gas side has lower mercury, then gas pressure $ P = P_{room} - (127 - 84) $? Wait, no: the difference in mercury levels. Let's see: in part a, the left (gas) side has mercury at 84, right at 127. So the difference is $ 127 - 84 = 43 $ mmHg. Since the gas pressure is less than room pressure (because right side is higher), so $ P = P_{room} - \Delta h $.
$ P_{room} = 730 $ mmHg, $ \Delta h = 127 - 84 = 43 $ mmHg.
## Step2: Calculate gas pressure.
$ P = 730 - 43 = 687 $ mmHg.
# Answer: 687 mmHg

### Problem 1b:
# Explanation:
## Step1: Mercury levels: left (open) at 26, right (gas) at 130. So difference $ \Delta h = 130 - 26 = 104 $ mmHg. Gas pressure is higher than room pressure (since right side is higher, gas pushes mercury up on its side), so $ P = P_{room} + \Delta h $.
$ P_{room} = 730 $ mmHg, $ \Delta h = 130 - 26 = 104 $ mmHg.
## Step2: Calculate.
$ P = 730 + 104 = 834 $ mmHg.
# Answer: 834 mmHg

### Problem 1c:
# Explanation:
## Step1: Mercury levels are equal (95 on both sides). So gas pressure equals room pressure.
$ P = P_{room} = 730 $ mmHg.
# Answer: 730 mmHg

### Problem 2a:
# Explanation:
## Step1: Mercury levels: left (open) at 95, right (gas) at 41. Difference $ \Delta h = 95 - 41 = 54 $ mmHg. Gas pressure is higher (since left side is higher, gas pushes mercury down on its side), so $ P = P_{room} + \Delta h $.
$ P_{room} = 733 $ mmHg, $ \Delta h = 95 - 41 = 54 $ mmHg.
## Step2: Calculate.
$ P = 733 + 54 = 787 $ mmHg.
# Answer: 787 mmHg

### Problem 2b:
# Explanation:
## Step1: Mercury levels: left (gas) at 104, right (open) at 31. Difference $ \Delta h = 104 - 31 = 73 $ mmHg. Gas pressure is higher (gas side mercury is higher), so $ P = P_{room} + \Delta h $? Wait, no: if gas side is 104, open side 31, then gas pressure is pushing mercury up on its side, so $ P = P_{room} + (104 - 31) $? Wait, no: the pressure at the bottom of the manometer is equal. So $ P_{gas} + 104 $ (mercury column on gas side) = $ P_{room} + 31 $ (mercury column on open side)? No, wait, mercury height: the difference is $ 104 - 31 = 73 $. Wait, maybe I got the direction wrong. Let's think: the open side has mercury at 31, gas side at 104. So the gas pressure is $ P_{room} + (104 - 31) $? Wait, no, the pressure from the gas plus the mercury column on the gas side equals the room pressure plus the mercury column on the open side. So $ P + 104 = P_{room} + 31 $? No, that would mean $ P = P_{room} - 73 $, but that would be lower, but gas side mercury is higher, which would mean gas pressure is lower? Wait, no, maybe the units are in mmHg, and the height is measured from the bottom. Let's re-express: the difference in height is $ 104 - 31 = 73 $ mmHg. If the gas side mercury is higher, that means the gas pressure is less than room pressure? Wait, no: if you have a manometer, when gas pressure is less than atmospheric, the atmospheric side (open) pushes mercury up on the gas side. Wait, in this case, gas side is 104, open side 31. So the open side has lower mercury, meaning gas pressure is less? Wait, no, mercury rises on the side with lower pressure. So if gas pressure is less than room pressure, mercury rises on the gas side. So the difference is $ 104 - 31 = 73 $ mmHg. So $ P = P_{room} - 73 $. $ P_{room} = 733 $, so $ 733 - 73 = 660 $ mmHg? Wait, that contradicts. Wait, maybe I mixed up the sides. Let's look at the diagram: in 2b, the gas is on the left, connected to a U-tube where left (gas) has mercury at 104, right (open) at 31. So the mercury is higher on the gas side, so gas pressure is less than room pressure. So the pressure from the room is pushing mercury up on the gas side. So the difference in height is $ 104 - 31 = 73 $ mmHg. So $ P = P_{room} - 73 = 733 - 73 = 660 $ mmHg. Wait, but let's check again. The formula for manometer: if the gas is connected to one side, and the other is open to atmosphere, then:

- If mercury is higher on the gas side: $ P_{gas} = P_{atm} - \Delta h $
- If mercury is higher on the open side: $ P_{gas} = P_{atm} + \Delta h $

In 2b, gas side mercury is 104, open side 31. So $ \Delta h = 104 - 31 = 73 $ mmHg (gas side higher). So $ P = 733 - 73 = 660 $ mmHg.

## Step1: Determine $ \Delta h = 104 - 31 = 73 $ mmHg.
## Step2: Calculate $ P = 733 - 73 = 660 $ mmHg.
# Answer: 660 mmHg

### Problem 2c:
# Explanation:
## Step1: Mercury levels: left (open) at 96, right (gas) at 138. Difference $ \Delta h = 138 - 96 = 42 $ mmHg. Gas side is higher, so gas pressure is less than room pressure? Wait, no: open side is 96, gas side 138. So mercury is higher on gas side, so $ P = P_{room} - \Delta h $. $ P_{room} = 733 $, $ \Delta h = 138 - 96 = 42 $.
## Step2: Calculate $ P = 733 - 42 = 691 $ mmHg? Wait, no, wait: if open side is 96, gas side 138, then the difference is 138 - 96 = 42, and since gas side is higher, gas pressure is lower, so $ P = 733 - 42 = 691 $? Wait, no, maybe I got the direction wrong. Wait, the pressure at the bottom of the U-tube: $ P_{gas} + 138 = P_{room} + 96 $? No, that would be $ P_{gas} = P_{room} + 96 - 138 = 733 - 42 = 691 $. Yes, that's correct. So $ P = 733 - (138 - 96) = 733 - 42 = 691 $ mmHg.
# Answer: 691 mmHg

### Problem 3:
# Brief Explanations:
Atmospheric pressure is the force per unit area exerted by the weight of the Earth’s atmosphere (air) on a surface. It is caused by the gravitational pull on the air molecules in the atmosphere, which have mass and are pulled towards the Earth’s surface, creating a pressure due to their weight.
# Answer: Atmospheric pressure is the pressure exerted by the weight of air in the Earth’s atmosphere on a surface. It is caused by the gravitational attraction pulling air molecules (with mass) towards the Earth, resulting in a force (weight) per unit area.

### Problem 4:
# Brief Explanations:
Atmospheric pressure is measured using a barometer (e.g., mercury barometer, aneroid barometer). A mercury barometer measures it by the height of a mercury column supported by atmospheric pressure (e.g., standard atmospheric pressure supports ~760 mmHg of mercury). Atmospheric pressure is not the same everywhere on Earth’s surface. It varies with altitude (decreases with increasing altitude, as there’s less air above), temperature (warmer air is less dense, so lower pressure), humidity (moist air is less dense than dry air, so lower pressure), and weather systems (e.g., low-pressure systems have rising air, high-pressure have sinking air).
# Answer: We measure atmospheric pressure using a barometer (e.g., mercury barometer, aneroid barometer). Atmospheric pressure is not the same everywhere on Earth’s surface; it varies with altitude, temperature, humidity, and weather conditions.

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QUESTION IMAGE

Question

Explanation:

Problem 1a:

Step2: Calculate gas pressure.

Step1: Mercury levels: left (open) at 26, right (gas) at 130. So difference \( \Delta h = 130 - 26 = 104 \) mmHg. Gas pressure is higher than room pressure (since right side is higher, gas pushes mercury up on its side), so \( P = P_{room} + \Delta h \).

Step2: Calculate.

Step1: Mercury levels are equal (95 on both sides). So gas pressure equals room pressure.

Answer:

Problem 1b: