Eilish Herron, of Paisley, was fuelling her Renault Clio at the forecourt in Linwood, at about 14:30 on Wednesday, when it was hit by a Ford Focus.
The 17-year-old died at the scene. The male Ford car driver was uninjured.
Eilish's former school, St Andrew's Academy, have also said she was "very popular" and "a wonderful young adult".
In a statement, Eilish's family said: "We are absolutely devastated by the loss of our beautiful daughter Eilish.
"We just cannot believe that we will not see her again. She was a lovely girl, a good daughter, sister, granddaughter and a great friend to those who knew her. She had so much to live for and we will miss her terribly.
"We are very gratefully for the thoughts and kind words already given, however, we would ask that we be allowed to have the time to grieve as a family at this very, very sad and difficult time."
Kevin Henry, head teacher at Eilish's former school in Paisley, said: "Eilish enjoyed six very successful and happy years in St Andrew's Academy and had left at the summer. She had been accepted to study nursing at Robert Gordon University.
"Eilish was a wonderful young adult and was very popular with both her peers and the staff of the school.
"She was a talented sportswoman and had been recognised in 2013 as Renfrewshire Young Sportsperson of the Year."
Mr Henry said Eilish had given "much of her own time to coaching younger students in the school".
"Eilish was a great role model for our pupils, her death is a tragic loss," he said.
"Staff and the school chaplain will be available to students who require any support. Eilish and her family will be in the thoughts and prayers of all in the school."
Meanwhile, police have asked anyone with information about the incident in which Eilish died to contact them.
A report on the circumstances will be submitted to the procurator fiscal.

The huge red crane crashed into a part of the Grand Mosque as it was filled with worshippers, less than two weeks before the annual Hajj pilgrimage.
Officials say strong winds and heavy rains caused the crane to fall.
Correspondents say there have previously been concerns about safety on Saudi construction sites.
The Grand Mosque, known as the Masjid al-Haram, is the largest mosque in the world and surrounds Islam's holiest place, the Kaaba.
At least 230 people were injured in the incident. It is unclear how many people were hurt by the collapse or the stampede that followed it.
Those killed are reported to include Indonesian, Indian, Iranian and Egyptian citizens.
The incident happened at 17:23 local time (14:23 GMT) on Friday.
Videos posted online showed the moment the structure collapsed, with a loud crash followed by panic and shouting. Bodies and blood could be seen on the floor of the mosque.
The head of Saudi Arabia's civil defence agency, Lt Sulayman Bin-Abdullah al-Amr, said an investigation was being carried out to assess the damage, and the "extent of the safety of these sites".
Essam al-Ghalib, a Jeddah-based journalist, said the crane fell through the outer ring of the Grand Mosque and punctured through the roof sending down tonnes of cement and debris onto people either praying or walking through.
Up to two million people are expected to arrive in Mecca for the Hajj from all over the world later this month.
Saudi officials say the crane disaster will not prevent the Hajj going ahead.
Irfan Al-Alawi, from the Islamic Heritage Research Foundation, told the BBC that the Grand Mosque is currently surrounded by 15 large cranes amid major redevelopment work.
"The entire area is like a salvage yard," Mr Al-Alawi said.
"Saudi Arabia has to re-think its health and safety strategy," he said, "as there were 800,000 people in the mosque area at the time of the accident."
The original parts of the Grand Mosque date back 1,400 years. Consisting of a large square surrounded by covered prayer areas, the building has since been extensively modernised, notably from the mid-20th Century.
Saudi authorities began a major expansion of the site last year to increase the area of the mosque by 400,000 square metres (4.3 million square feet), to allow it to accommodate up to 2.2 million people at once.
The family of a Renfrewshire teenager who died after a collision between two cars at an Asda petrol station have said they are "devastated" by her loss.
[NEXT_CONCEPT]
Saudi Arabia has begun an investigation into why a crane collapsed in the Muslim holy city of Mecca, killing at least 107 people.