a packaging engineer is working on a new design for cold packs. A burst chamber in the pack will contain 14.0 mL of water, which will be released and used to dissolve ammonia nitrate.
a) If the solubility of NH4NO3 is 190g/100g H2O, what mass of this compound should be used with this amount of water?
b)The design specifications indicate that these chemicals can comprise no more than 35% of the mass of the product. What would the product weigh if it just meets these design specs?
You have 14g water.
190/100=mass/14 solve for mass smmonium nitrate.
product mass= (14g+massabove)/.35
Your use of weight and mass is rather loose. weight is not mass, and mass is not weight.
116 g
A)46.4g
B)150g
a) Ah, the packaging engineer and their chemistry adventures! Alright, let's crunch some numbers. We know the burst chamber will contain 14.0 mL of water. The solubility of NH4NO3 is given as 190g/100g H2O.
To find the mass of NH4NO3, we'll use a proportion. 190g NH4NO3 corresponds to 100g of water. So, for 14.0 mL of water, we can set up the proportion:
190g NH4NO3 / 100g H2O = x / 14.0g H2O
Cross-multiplying, we find:
x = (190g NH4NO3 * 14.0g H2O) / 100g H2O
x = 26.6g NH4NO3
So, you should use approximately 26.6 grams of NH4NO3 with 14.0 mL of water.
b) Now, onto the weight of the product. Design specs state that the chemicals should not exceed 35% of the product's mass. Since we already know the mass of NH4NO3 is 26.6g, we can calculate the maximum mass using the proportion:
35g chemical / 100g product = 26.6g NH4NO3 / x
Cross-multiplying gives us:
35g product * x = 100g product * 26.6g NH4NO3
35x = 2660
x = 76g
So, the product should weigh approximately 76 grams if it just meets the design specs.
And there you have it, a tale of water, chemical solubility, and product weight. Hope this brings a smile to your face!
To find the mass of NH4NO3 that should be used with 14.0 mL of water:
a) First, we need to determine the mass of water in grams. Since the density of water is approximately 1 g/mL, the mass of 14.0 mL of water is 14.0 grams.
Next, we need to find the mass of NH4NO3 that can be dissolved in 14.0 grams of water. According to the given solubility, NH4NO3 has a solubility of 190g/100g H2O. This means that 100 grams of water can dissolve 190 grams of NH4NO3.
Since we have 14.0 grams of water, we can use a proportion to find the mass of NH4NO3:
(14.0 g water / 100 g water) * 190 g NH4NO3 = 26.6 g NH4NO3
So, the mass of NH4NO3 that should be used with 14.0 mL of water is 26.6 grams.
Now let's find the weight of the product if it meets the design specifications:
b) The design specifies that the chemicals can comprise no more than 35% of the total mass of the product. To find the weight of the product, we need to know the mass of NH4NO3 and the mass of water.
From part a, we know that the mass of NH4NO3 is 26.6 grams. The mass of water is 14.0 grams.
To calculate the total mass of the product, we need to determine the mass of other components as well. Let's assume the mass of these components is "x" grams.
According to the design specifications, the chemicals (NH4NO3 + water) together should comprise no more than 35% of the total mass. This means that the total mass of chemicals should be no more than 35% of the total mass of the product.
Setting up an equation:
26.6 g NH4NO3 + 14.0 g water + x g other components = 0.35 * (26.6 g NH4NO3 + 14.0 g water + x g other components)
Now we can solve for x (mass of other components):
26.6g NH4NO3 + 14.0g water + x = 0.35 * (26.6g NH4NO3 + 14.0g water + x)
Simplifying the equation:
26.6g NH4NO3 + 14.0g water + x = 9.31g NH4NO3 + 4.9g water + 0.35x
Now solve for x:
0.65x = 9.31g NH4NO3 + 4.9g water - 26.6g NH4NO3 - 14.0g water
0.65x = -12.69g NH4NO3 - 9.1g water
x = (-12.69g NH4NO3 - 9.1g water) / 0.65
x ≈ -37.45g
Since mass cannot be negative, it means that the mass of other components should be negligible for the product to meet the design specifications. Therefore, the weight of the product, in this case, would only be the combined weight of NH4NO3 and water, which is approximately 40.6 grams (26.6 grams NH4NO3 + 14.0 grams water).
a) 26.6g
b) 14.21g